/usr/bin/diffoscope --timeout 7200 --html /srv/reproducible-results/rbuild-debian/r-b-build.0FY7SZac/statsmodels_0.14.4+dfsg-1.diffoscope.html --text /srv/reproducible-results/rbuild-debian/r-b-build.0FY7SZac/statsmodels_0.14.4+dfsg-1.diffoscope.txt --json /srv/reproducible-results/rbuild-debian/r-b-build.0FY7SZac/statsmodels_0.14.4+dfsg-1.diffoscope.json --profile=- /srv/reproducible-results/rbuild-debian/r-b-build.0FY7SZac/b1/statsmodels_0.14.4+dfsg-1_arm64.changes /srv/reproducible-results/rbuild-debian/r-b-build.0FY7SZac/b2/statsmodels_0.14.4+dfsg-1

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/srv/reproducible-results/rbuild-debian/r-b-build.0FY7SZac/b2/statsmodels_0.14.4+dfsg-1_arm64.changes ¶

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python-statsmodels-doc_0.14.4+dfsg-1_all.deb ¶

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file list ¶

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control.tar.xz ¶

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control.tar ¶

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./control ¶

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./md5sums ¶

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./md5sums ¶

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data.tar ¶

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1	·~~9f0177de67789~~03da~~7a80~~a~~149d6d63ca~~·39~~577148~~·doc·optional·python-statsmodels-doc_0.14.4+dfsg-1_all.deb	1	·2dc3d236d9156080a1dafafbe4ae2c8b·39606220·doc·optional·python-statsmodels-doc_0.14.4+dfsg-1_all.deb
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1	-rw-r--r--···0········0········0········4·2024-10-05·10:43:25.000000·debian-binary	1	-rw-r--r--···0········0········0········4·2024-10-05·10:43:25.000000·debian-binary
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1	Package:·python-statsmodels-doc	1	Package:·python-statsmodels-doc
2	Source:·statsmodels	2	Source:·statsmodels
3	Version:·0.14.4+dfsg-1	3	Version:·0.14.4+dfsg-1
4	Architecture:·all	4	Architecture:·all
5	Maintainer:·Debian·Science·Maintainers·<debian-science-maintainers@lists.alioth.debian.org>	5	Maintainer:·Debian·Science·Maintainers·<debian-science-maintainers@lists.alioth.debian.org>
6	Installed-Size:·156039	6	Installed-Size:·156037
7	Depends:·libjs-sphinxdoc·(>=·7.4),·libjs-requirejs,·libjs-mathjax	7	Depends:·libjs-sphinxdoc·(>=·7.4),·libjs-requirejs,·libjs-mathjax
8	Suggests:·python3-statsmodels,·python3-doc,·python-numpy-doc,·python-patsy-doc,·python-pandas-doc,·python-scipy-doc	8	Suggests:·python3-statsmodels,·python3-doc,·python-numpy-doc,·python-patsy-doc,·python-pandas-doc,·python-scipy-doc
9	Breaks:·python-scikits-statsmodels-doc,·python-scikits.statsmodels-doc,·python-statsmodels·(<<·0.9.0-3~)	9	Breaks:·python-scikits-statsmodels-doc,·python-scikits.statsmodels-doc,·python-statsmodels·(<<·0.9.0-3~)
10	Replaces:·python-scikits-statsmodels-doc,·python-scikits.statsmodels-doc,·python-statsmodels·(<<·0.9.0-3~)	10	Replaces:·python-scikits-statsmodels-doc,·python-scikits.statsmodels-doc,·python-statsmodels·(<<·0.9.0-3~)
11	Section:·doc	11	Section:·doc
12	Priority:·optional	12	Priority:·optional
13	Homepage:·https://www.statsmodels.org	13	Homepage:·https://www.statsmodels.org


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32	············"source":·[	32	············"source":·[
Offset 39, 18 lines modified		Offset 39, 18 lines modified
39	············]	39	············]
40	········},	40	········},
41	········{	41	········{
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43	············"execution_count":·2,	43	············"execution_count":·2,
44	············"metadata":·{	44	············"metadata":·{
45	················"execution":·{	45	················"execution":·{
46	····················"iopub.execute_input":·"2025-12-09T22:24:38.~~210551~~Z",	46	····················"iopub.execute_input":·"2024-11-06T18:40:44.743494Z",
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49	····················"shell.execute_reply":·"2025-12-09T22:24:38.~~233407~~Z"	49	····················"shell.execute_reply":·"2024-11-06T18:40:44.758263Z"
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55	············"outputs":·[],	55	············"outputs":·[],
56	············"source":·[	56	············"source":·[
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63	········{	63	········{
64	············"cell_type":·"code",	64	············"cell_type":·"code",
65	············"execution_count":·3,	65	············"execution_count":·3,
66	············"metadata":·{	66	············"metadata":·{
67	················"execution":·{	67	················"execution":·{
68	····················"iopub.execute_input":·"2025-12-09T22:24:38.~~254382~~Z",	68	····················"iopub.execute_input":·"2024-11-06T18:40:44.775277Z",
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71	····················"shell.execute_reply":·"2025-12-09T22:24:38.725829Z"	71	····················"shell.execute_reply":·"2024-11-06T18:40:45.158238Z"
72	················},	72	················},
73	················"jupyter":·{	73	················"jupyter":·{
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75	················}	75	················}
76	············},	76	············},
77	············"outputs":·[	77	············"outputs":·[
78	················{	78	················{


Offset 120, 15 lines modified		Offset 120, 15 lines modified
120	</div>	120	</div>
121	</div>	121	</div>
122	<div·class="nboutput·docutils·container">	122	<div·class="nboutput·docutils·container">
123	<div·class="prompt·empty·docutils·container">	123	<div·class="prompt·empty·docutils·container">
124	</div>	124	</div>
125	<div·class="output_area·stderr·docutils·container">	125	<div·class="output_area·stderr·docutils·container">
126	<div·class="highlight"><pre>	126	<div·class="highlight"><pre>
127	/tmp/ipykernel_28~~99008~~/2751177292.py:28:·FutureWarning:·The·'delim_whitespace'·keyword·in·pd.read_csv·is·deprecated·and·will·be·removed·in·a·future·version.·Use·``sep='\s+'``·instead	127	/tmp/ipykernel_2848951/2751177292.py:28:·FutureWarning:·The·'delim_whitespace'·keyword·in·pd.read_csv·is·deprecated·and·will·be·removed·in·a·future·version.·Use·``sep='\s+'``·instead
128	··data·=·pd.read_csv(StringIO(data),·delim_whitespace=True).astype(float)	128	··data·=·pd.read_csv(StringIO(data),·delim_whitespace=True).astype(float)
129	</pre></div></div>	129	</pre></div></div>
130	</div>	130	</div>
131	<div·class="nboutput·nblast·docutils·container">	131	<div·class="nboutput·nblast·docutils·container">
132	<div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[2]:	132	<div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[2]:
133	</pre></div>	133	</pre></div>
134	</div>	134	</div>


Offset 56, 15 lines modified		Offset 56, 15 lines modified
56	except·ImportError:	56	except·ImportError:
57	····from·io·import·StringIO	57	····from·io·import·StringIO
58	data·=·pd.read_csv(StringIO(data),·delim_whitespace=True).astype(float)	58	data·=·pd.read_csv(StringIO(data),·delim_whitespace=True).astype(float)

59	#·Note:·for·the·results·we·compare·with·the·paper·here,·they·drop·the·first	59	#·Note:·for·the·results·we·compare·with·the·paper·here,·they·drop·the·first
60	four·points	60	four·points
61	data.head()	61	data.head()
62	/tmp/ipykernel_28~~99008~~/2751177292.py:28:·FutureWarning:·The·'delim_whitespace'	62	/tmp/ipykernel_2848951/2751177292.py:28:·FutureWarning:·The·'delim_whitespace'
63	keyword·in·pd.read_csv·is·deprecated·and·will·be·removed·in·a·future·version.	63	keyword·in·pd.read_csv·is·deprecated·and·will·be·removed·in·a·future·version.
64	Use·``sep='\s+'``·instead	64	Use·``sep='\s+'``·instead
65	··data·=·pd.read_csv(StringIO(data),·delim_whitespace=True).astype(float)	65	··data·=·pd.read_csv(StringIO(data),·delim_whitespace=True).astype(float)
66	[2]:	66	[2]:
67	·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·	67	·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·
68	\|_\x8·_\x8\|_\x8·_\x8·_\x8·_\x8·_\x8x\x8x_\x8\|_\x8·_\x8·_\x8·_\x8·_\x8y\x8y_\x8\|_\x8y\x8y_\x8_\x8__\x8e\x8e_\x8r\x8r_\x8r\x8r\|	68	\|_\x8·_\x8\|_\x8·_\x8·_\x8·_\x8·_\x8x\x8x_\x8\|_\x8·_\x8·_\x8·_\x8·_\x8y\x8y_\x8\|_\x8y\x8y_\x8_\x8__\x8e\x8e_\x8r\x8r_\x8r\x8r\|
69	\|_\x80\x80_\x8\|_\x82_\x80_\x81_\x8._\x80_\x8\|_\x85_\x89_\x82_\x8._\x80_\x8\|_\x86_\x81_\x8._\x80_\x8·\|	69	\|_\x80\x80_\x8\|_\x82_\x80_\x81_\x8._\x80_\x8\|_\x85_\x89_\x82_\x8._\x80_\x8\|_\x86_\x81_\x8._\x80_\x8·\|


Offset 19, 18 lines modified		Offset 19, 18 lines modified
19	············]	19	············]
20	········},	20	········},
21	········{	21	········{
22	············"cell_type":·"code",	22	············"cell_type":·"code",
23	············"execution_count":·1,	23	············"execution_count":·1,
24	············"metadata":·{	24	············"metadata":·{
25	················"execution":·{	25	················"execution":·{
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29	····················"shell.execute_reply":·"2025-12-09T22:24:36.~~697~~465Z"	29	····················"shell.execute_reply":·"2024-11-06T18:40:43.742409Z"
30	················},	30	················},
31	················"jupyter":·{	31	················"jupyter":·{
32	····················"outputs_hidden":·false	32	····················"outputs_hidden":·false
33	················}	33	················}
34	············},	34	············},
35	············"outputs":·[],	35	············"outputs":·[],
36	············"source":·[	36	············"source":·[
Offset 62, 29 lines modified		Offset 62, 29 lines modified
62	············]	62	············]
63	········},	63	········},
64	········{	64	········{
65	············"cell_type":·"code",	65	············"cell_type":·"code",
66	············"execution_count":·2,	66	············"execution_count":·2,
67	············"metadata":·{	67	············"metadata":·{
68	················"execution":·{	68	················"execution":·{
69	····················"iopub.execute_input":·"2025-12-09T22:24:36.7~~043~~87Z",	69	····················"iopub.execute_input":·"2024-11-06T18:40:43.747482Z",
70	····················"iopub.status.busy":·"2025-12-09T22:24:36.7~~03959~~Z",	70	····················"iopub.status.busy":·"2024-11-06T18:40:43.747062Z",
71	····················"iopub.status.idle":·"2025-12-09T22:24:36.~~754153~~Z",	71	····················"iopub.status.idle":·"2024-11-06T18:40:43.802970Z",
72	····················"shell.execute_reply":·"2025-12-09T22:24:36.~~753450~~Z"	72	····················"shell.execute_reply":·"2024-11-06T18:40:43.802247Z"
73	················},	73	················},
74	················"jupyter":·{	74	················"jupyter":·{
75	····················"outputs_hidden":·false	75	····················"outputs_hidden":·false
76	················}	76	················}
77	············},	77	············},
78	············"outputs":·[	78	············"outputs":·[
79	················{	79	················{
80	····················"name":·"stderr",	80	····················"name":·"stderr",
81	····················"output_type":·"stream",	81	····················"output_type":·"stream",
82	····················"text":·[	82	····················"text":·[
83	························"/tmp/ipykernel_28~~99008~~/2751177292.py:28:·FutureWarning:·The·'delim_whitespace'·keyword·in·pd.read_csv·is·deprecated·and·will·be·removed·in·a·future·version.·Use·``sep='\\s+'``·instead\n",	83	························"/tmp/ipykernel_2848951/2751177292.py:28:·FutureWarning:·The·'delim_whitespace'·keyword·in·pd.read_csv·is·deprecated·and·will·be·removed·in·a·future·version.·Use·``sep='\\s+'``·instead\n",
84	························"··data·=·pd.read_csv(StringIO(data),·delim_whitespace=True).astype(float)\n"	84	························"··data·=·pd.read_csv(StringIO(data),·delim_whitespace=True).astype(float)\n"
85	····················]	85	····················]
86	················},	86	················},
87	················{	87	················{
88	····················"data":·{	88	····················"data":·{
89	························"text/html":·[	89	························"text/html":·[
90	····························"<div>\n",	90	····························"<div>\n",
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211	············"cell_type":·"code",	211	············"cell_type":·"code",
212	············"execution_count":·3,	212	············"execution_count":·3,
213	············"metadata":·{	213	············"metadata":·{
214	················"execution":·{	214	················"execution":·{
215	····················"iopub.execute_input":·"2025-12-09T22:24:36.~~76029~~9Z",	215	····················"iopub.execute_input":·"2024-11-06T18:40:43.807019Z",
216	····················"iopub.status.busy":·"2025-12-09T22:24:36.~~760010~~Z",	216	····················"iopub.status.busy":·"2024-11-06T18:40:43.806733Z",
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218	····················"shell.execute_reply":·"2025-12-09T22:24:36.8~~05450~~Z"	218	····················"shell.execute_reply":·"2024-11-06T18:40:43.842239Z"
219	················},	219	················},
220	················"jupyter":·{	220	················"jupyter":·{
221	····················"outputs_hidden":·false	221	····················"outputs_hidden":·false
222	················}	222	················}
223	············},	223	············},
224	············"outputs":·[	224	············"outputs":·[
225	················{	225	················{
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271	············]	271	············]
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273	········{	273	········{
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276	············"metadata":·{	276	············"metadata":·{
277	················"execution":·{	277	················"execution":·{
278	····················"iopub.execute_input":·"2025-12-09T22:24:36.8~~1438~~7Z",	278	····················"iopub.execute_input":·"2024-11-06T18:40:43.846997Z",
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286	············},	286	············},
287	············"outputs":·[	287	············"outputs":·[
288	················{	288	················{
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329	····················"iopub.status.busy":·"2025-12-09T22:24:36.8~~460~~78Z",	329	····················"iopub.status.busy":·"2024-11-06T18:40:43.870571Z",
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332	················},	332	················},
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372	············]	372	············]
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89	········},	89	········},
90	········{	90	········{
91	············"cell_type":·"code",	91	············"cell_type":·"code",
92	············"execution_count":·4,	92	············"execution_count":·4,
93	············"metadata":·{	93	············"metadata":·{
94	················"execution":·{	94	················"execution":·{
95	····················"iopub.execute_input":·"2025-12-09T22:24:32.~~194541~~Z",	95	····················"iopub.execute_input":·"2024-11-06T18:40:37.230350Z",
96	····················"iopub.status.busy":·"2025-12-09T22:24:32.~~194~~242Z",	96	····················"iopub.status.busy":·"2024-11-06T18:40:37.230024Z",
97	····················"iopub.status.idle":·"2025-12-09T22:24:32.206095Z",	97	····················"iopub.status.idle":·"2024-11-06T18:40:37.243065Z",
98	····················"shell.execute_reply":·"2025-12-09T22:24:32.2~~05419~~Z"	98	····················"shell.execute_reply":·"2024-11-06T18:40:37.242392Z"
99	················}	99	················}
100	············},	100	············},
101	············"outputs":·[	101	············"outputs":·[
102	················{	102	················{
103	····················"name":·"stdout",	103	····················"name":·"stdout",
104	····················"output_type":·"stream",	104	····················"output_type":·"stream",
105	····················"text":·[	105	····················"text":·[
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140	········},	140	········},
141	········{	141	········{
142	············"cell_type":·"code",	142	············"cell_type":·"code",
143	············"execution_count":·5,	143	············"execution_count":·5,
144	············"metadata":·{	144	············"metadata":·{
145	················"execution":·{	145	················"execution":·{
146	····················"iopub.execute_input":·"2025-12-09T22:24:32.2~~12238~~Z",	146	····················"iopub.execute_input":·"2024-11-06T18:40:37.246941Z",
147	····················"iopub.status.busy":·"2025-12-09T22:24:32.2~~119~~45Z",	147	····················"iopub.status.busy":·"2024-11-06T18:40:37.246647Z",
148	····················"iopub.status.idle":·"2025-12-09T22:24:32.246418Z",	148	····················"iopub.status.idle":·"2024-11-06T18:40:37.294947Z",
149	····················"shell.execute_reply":·"2025-12-09T22:24:32.245462Z"	149	····················"shell.execute_reply":·"2024-11-06T18:40:37.294243Z"
150	················}	150	················}
151	············},	151	············},
152	············"outputs":·[],	152	············"outputs":·[],
153	············"source":·[	153	············"source":·[
154	················"dta·=·sm.datasets.fair.load_pandas().data"	154	················"dta·=·sm.datasets.fair.load_pandas().data"
155	············]	155	············]
156	········},	156	········},
157	········{	157	········{
158	············"cell_type":·"code",	158	············"cell_type":·"code",
159	············"execution_count":·6,	159	············"execution_count":·6,
160	············"metadata":·{	160	············"metadata":·{
161	················"execution":·{	161	················"execution":·{
162	····················"iopub.execute_input":·"2025-12-09T22:24:32.2~~54390~~Z",	162	····················"iopub.execute_input":·"2024-11-06T18:40:37.299127Z",
163	····················"iopub.status.busy":·"2025-12-09T22:24:32.2~~54078~~Z",	163	····················"iopub.status.busy":·"2024-11-06T18:40:37.298827Z",
164	····················"iopub.status.idle":·"2025-12-09T22:24:32.286690Z",	164	····················"iopub.status.idle":·"2024-11-06T18:40:37.338965Z",
165	····················"shell.execute_reply":·"2025-12-09T22:24:32.285408Z"	165	····················"shell.execute_reply":·"2024-11-06T18:40:37.338242Z"
166	················}	166	················}
167	············},	167	············},
168	············"outputs":·[	168	············"outputs":·[
169	················{	169	················{
170	····················"name":·"stdout",	170	····················"name":·"stdout",
171	····················"output_type":·"stream",	171	····················"output_type":·"stream",
172	····················"text":·[	172	····················"text":·[
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203	········},	203	········},
204	········{	204	········{
205	············"cell_type":·"code",	205	············"cell_type":·"code",
206	············"execution_count":·7,	206	············"execution_count":·7,
207	············"metadata":·{	207	············"metadata":·{
208	················"execution":·{	208	················"execution":·{
209	····················"iopub.execute_input":·"2025-12-09T22:24:32.~~294613~~Z",	209	····················"iopub.execute_input":·"2024-11-06T18:40:37.347002Z",
210	····················"iopub.status.busy":·"2025-12-09T22:24:32.~~29433~~5Z",	210	····················"iopub.status.busy":·"2024-11-06T18:40:37.346705Z",
211	····················"iopub.status.idle":·"2025-12-09T22:24:32.382~~126~~Z",	211	····················"iopub.status.idle":·"2024-11-06T18:40:37.442975Z",
212	····················"shell.execute_reply":·"2025-12-09T22:24:32.~~381420~~Z"	212	····················"shell.execute_reply":·"2024-11-06T18:40:37.442254Z"
213	················}	213	················}
214	············},	214	············},
215	············"outputs":·[	215	············"outputs":·[
216	················{	216	················{
217	····················"name":·"stdout",	217	····················"name":·"stdout",
218	····················"output_type":·"stream",	218	····················"output_type":·"stream",
219	····················"text":·[	219	····················"text":·[
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10	············]	10	············]
11	········},	11	········},
12	········{	12	········{
13	············"cell_type":·"code",	13	············"cell_type":·"code",
14	············"execution_count":·1,	14	············"execution_count":·1,
15	············"metadata":·{	15	············"metadata":·{
16	················"execution":·{	16	················"execution":·{
17	····················"iopub.execute_input":·"2025-12-09T22:24:24.~~87833~~0Z",	17	····················"iopub.execute_input":·"2024-11-06T18:40:29.903160Z",
18	····················"iopub.status.busy":·"2025-12-09T22:24:24.~~878064~~Z",	18	····················"iopub.status.busy":·"2024-11-06T18:40:29.902888Z",
19	····················"iopub.status.idle":·"2025-12-09T22:24:27.~~445470~~Z",	19	····················"iopub.status.idle":·"2024-11-06T18:40:32.193583Z",
20	····················"shell.execute_reply":·"2025-12-09T22:24:27.~~433466~~Z"	20	····················"shell.execute_reply":·"2024-11-06T18:40:32.190308Z"
21	················}	21	················}
22	············},	22	············},
23	············"outputs":·[],	23	············"outputs":·[],
24	············"source":·[	24	············"source":·[
25	················"import·numpy·as·np\n",	25	················"import·numpy·as·np\n",
26	················"from·scipy.stats.distributions·import·norm\n",	26	················"from·scipy.stats.distributions·import·norm\n",
27	················"from·statsmodels.base.distributed_estimation·import·DistributedModel\n",	27	················"from·statsmodels.base.distributed_estimation·import·DistributedModel\n",
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61	············]	61	············]
62	········},	62	········},
63	········{	63	········{
64	············"cell_type":·"code",	64	············"cell_type":·"code",
65	············"execution_count":·2,	65	············"execution_count":·2,
66	············"metadata":·{	66	············"metadata":·{
67	················"execution":·{	67	················"execution":·{
68	····················"iopub.execute_input":·"2025-12-09T22:24:27.~~454565~~Z",	68	····················"iopub.execute_input":·"2024-11-06T18:40:32.197720Z",
69	····················"iopub.status.busy":·"2025-12-09T22:24:27.~~454175~~Z",	69	····················"iopub.status.busy":·"2024-11-06T18:40:32.197333Z",
70	····················"iopub.status.idle":·"2025-12-09T22:24:27.~~489463~~Z",	70	····················"iopub.status.idle":·"2024-11-06T18:40:32.210937Z",
71	····················"shell.execute_reply":·"2025-12-09T22:24:27.~~477454~~Z"	71	····················"shell.execute_reply":·"2024-11-06T18:40:32.210239Z"
72	················}	72	················}
73	············},	73	············},
74	············"outputs":·[],	74	············"outputs":·[],
75	············"source":·[	75	············"source":·[
76	················"X·=·np.random.normal(size=(1000,·25))\n",	76	················"X·=·np.random.normal(size=(1000,·25))\n",
77	················"beta·=·np.random.normal(size=25)\n",	77	················"beta·=·np.random.normal(size=25)\n",
78	················"beta·*=·np.random.randint(0,·2,·size=25)\n",	78	················"beta·*=·np.random.randint(0,·2,·size=25)\n",
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88	············]	88	············]
89	········},	89	········},
90	········{	90	········{
91	············"cell_type":·"code",	91	············"cell_type":·"code",
92	············"execution_count":·3,	92	············"execution_count":·3,
93	············"metadata":·{	93	············"metadata":·{
94	················"execution":·{	94	················"execution":·{
95	····················"iopub.execute_input":·"2025-12-09T22:24:2~~7.49~~8419Z",	95	····················"iopub.execute_input":·"2024-11-06T18:40:32.214861Z",
96	····················"iopub.status.busy":·"2025-12-09T22:24:27.~~498128~~Z",	96	····················"iopub.status.busy":·"2024-11-06T18:40:32.214570Z",
97	····················"iopub.status.idle":·"2025-12-09T22:24:28.218157Z",	97	····················"iopub.status.idle":·"2024-11-06T18:40:32.822484Z",
98	····················"shell.execute_reply":·"2025-12-09T22:24:28.21~~7471~~Z"	98	····················"shell.execute_reply":·"2024-11-06T18:40:32.819922Z"
99	················}	99	················}
100	············},	100	············},
101	············"outputs":·[],	101	············"outputs":·[],
102	············"source":·[	102	············"source":·[
103	················"debiased_OLS_mod·=·DistributedModel(m)\n",	103	················"debiased_OLS_mod·=·DistributedModel(m)\n",
104	················"debiased_OLS_fit·=·debiased_OLS_mod.fit(\n",	104	················"debiased_OLS_fit·=·debiased_OLS_mod.fit(\n",
105	················"····zip(_endog_gen(y,·m),·_exog_gen(X,·m)),·fit_kwds={\"alpha\":·0.2}\n",	105	················"····zip(_endog_gen(y,·m),·_exog_gen(X,·m)),·fit_kwds={\"alpha\":·0.2}\n",
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114	············]	114	············]
115	········},	115	········},
116	········{	116	········{
117	············"cell_type":·"code",	117	············"cell_type":·"code",
118	············"execution_count":·4,	118	············"execution_count":·4,
119	············"metadata":·{	119	············"metadata":·{
120	················"execution":·{	120	················"execution":·{
121	····················"iopub.execute_input":·"2025-12-09T22:24:28.226~~421~~Z",	121	····················"iopub.execute_input":·"2024-11-06T18:40:32.826292Z",
122	····················"iopub.status.busy":·"2025-12-09T22:24:28.22~~6145~~Z",	122	····················"iopub.status.busy":·"2024-11-06T18:40:32.825989Z",
123	····················"iopub.status.idle":·"2025-12-09T22:24:29.~~77813~~0Z",	123	····················"iopub.status.idle":·"2024-11-06T18:40:33.994940Z",
124	····················"shell.execute_reply":·"2025-12-09T22:24:29.~~777449~~Z"	124	····················"shell.execute_reply":·"2024-11-06T18:40:33.994312Z"
125	················}	125	················}
126	············},	126	············},
127	············"outputs":·[],	127	············"outputs":·[],
128	············"source":·[	128	············"source":·[
129	················"from·statsmodels.genmod.generalized_linear_model·import·GLM\n",	129	················"from·statsmodels.genmod.generalized_linear_model·import·GLM\n",
130	················"from·statsmodels.genmod.families·import·Gaussian\n",	130	················"from·statsmodels.genmod.families·import·Gaussian\n",
131	················"\n",	131	················"\n",
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145	············]	145	············]
146	········},	146	········},
147	········{	147	········{
148	············"cell_type":·"code",	148	············"cell_type":·"code",
149	············"execution_count":·5,	149	············"execution_count":·5,
150	············"metadata":·{	150	············"metadata":·{
151	················"execution":·{	151	················"execution":·{
152	····················"iopub.execute_input":·"2025-12-09T22:24:29.~~784253~~Z",	152	····················"iopub.execute_input":·"2024-11-06T18:40:33.998811Z",
153	····················"iopub.status.busy":·"2025-12-09T22:24:29.~~783979~~Z",	153	····················"iopub.status.busy":·"2024-11-06T18:40:33.998521Z",
154	····················"iopub.status.idle":·"2025-12-09T22:24:30.178~~148~~Z",	154	····················"iopub.status.idle":·"2024-11-06T18:40:34.238883Z",
155	····················"shell.execute_reply":·"2025-12-09T22:24:30.~~177449~~Z"	155	····················"shell.execute_reply":·"2024-11-06T18:40:34.238231Z"
156	················}	156	················}
157	············},	157	············},
158	············"outputs":·[],	158	············"outputs":·[],
159	············"source":·[	159	············"source":·[
160	················"from·statsmodels.base.distributed_estimation·import·_est_regularized_naive,·_join_naive\n",	160	················"from·statsmodels.base.distributed_estimation·import·_est_regularized_naive,·_join_naive\n",
161	················"\n",	161	················"\n",
162	················"\n",	162	················"\n",
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176	············]	176	············]
177	········},	177	········},
178	········{	178	········{
179	············"cell_type":·"code",	179	············"cell_type":·"code",
180	············"execution_count":·6,	180	············"execution_count":·6,
181	············"metadata":·{	181	············"metadata":·{
182	················"execution":·{	182	················"execution":·{
183	····················"iopub.execute_input":·"2025-12-09T22:24:30.~~184199~~Z",	183	····················"iopub.execute_input":·"2024-11-06T18:40:34.242810Z",
184	····················"iopub.status.busy":·"2025-12-09T22:24:30.~~183926~~Z",	184	····················"iopub.status.busy":·"2024-11-06T18:40:34.242531Z",
185	····················"iopub.status.idle":·"2025-12-09T22:24:30.226149Z",	185	····················"iopub.status.idle":·"2024-11-06T18:40:34.266859Z",
186	····················"shell.execute_reply":·"2025-12-09T22:24:30.2~~25447~~Z"	186	····················"shell.execute_reply":·"2024-11-06T18:40:34.266213Z"
187	················}	187	················}
188	············},	188	············},
189	············"outputs":·[],	189	············"outputs":·[],
190	············"source":·[	190	············"source":·[
191	················"from·statsmodels.base.distributed_estimation·import·(\n",	191	················"from·statsmodels.base.distributed_estimation·import·(\n",
192	················"····_est_unregularized_naive,\n",	192	················"····_est_unregularized_naive,\n",
193	················"····DistributedResults,\n",	193	················"····DistributedResults,\n",


Offset 555, 14 lines modified		Offset 555, 23 lines modified
555	<span·class="n">fit</span><span·class="o">.</span><span·class="n">fittedvalues</span><span·class="o">.</span><span·class="n">plot</span><span·class="p">(</span><span·class="n">label</span><span·class="o">=</span><span·class="s2">"statsmodels·fit"</span><span·class="p">)</span>	555	<span·class="n">fit</span><span·class="o">.</span><span·class="n">fittedvalues</span><span·class="o">.</span><span·class="n">plot</span><span·class="p">(</span><span·class="n">label</span><span·class="o">=</span><span·class="s2">"statsmodels·fit"</span><span·class="p">)</span>
556	<span·class="n">fit_R</span><span·class="o">.</span><span·class="n">fittedvalues</span><span·class="o">.</span><span·class="n">plot</span><span·class="p">(</span><span·class="n">label</span><span·class="o">=</span><span·class="s2">"R·fit"</span><span·class="p">,</span>·<span·class="n">linestyle</span><span·class="o">=</span><span·class="s2">"--"</span><span·class="p">)</span>	556	<span·class="n">fit_R</span><span·class="o">.</span><span·class="n">fittedvalues</span><span·class="o">.</span><span·class="n">plot</span><span·class="p">(</span><span·class="n">label</span><span·class="o">=</span><span·class="s2">"R·fit"</span><span·class="p">,</span>·<span·class="n">linestyle</span><span·class="o">=</span><span·class="s2">"--"</span><span·class="p">)</span>
557	<span·class="n">plt</span><span·class="o">.</span><span·class="n">legend</span><span·class="p">()</span>	557	<span·class="n">plt</span><span·class="o">.</span><span·class="n">legend</span><span·class="p">()</span>
558	</pre></div>	558	</pre></div>
559	</div>	559	</div>
560	</div>	560	</div>
561	<div·class="nboutput·docutils·container">	561	<div·class="nboutput·docutils·container">
		562	<div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[9]:
		563	</pre></div>
		564	</div>
		565	<div·class="output_area·docutils·container">
		566	<div·class="highlight"><pre>
		567	<matplotlib.legend.Legend·at·0xadde5de1e8ed>
		568	</pre></div></div>
		569	</div>
		570	<div·class="nboutput·docutils·container">
562	<div·class="prompt·empty·docutils·container">	571	<div·class="prompt·empty·docutils·container">
563	</div>	572	</div>
564	<div·class="output_area·docutils·container">	573	<div·class="output_area·docutils·container">
565	<div·class="highlight"><pre>	574	<div·class="highlight"><pre>
566	RUNNING·THE·L-BFGS-B·CODE	575	RUNNING·THE·L-BFGS-B·CODE

567	·············*	576	·············*
Offset 755, 23 lines modified		Offset 764, 14 lines modified
755	···N····Tit·····Tnf··Tnint··Skip··Nact·····Projg········F	764	···N····Tit·····Tnf··Tnint··Skip··Nact·····Projg········F
756	····9·····82····102·····90·····0·····1···1.643D-05···2.245D+00	765	····9·····82····102·····90·····0·····1···1.643D-05···2.245D+00
757	··F·=···2.2445124982934956	766	··F·=···2.2445124982934956

758	CONVERGENCE:·REL_REDUCTION_OF_F_<=_FACTR*EPSMCH	767	CONVERGENCE:·REL_REDUCTION_OF_F_<=_FACTR*EPSMCH
759	</pre></div></div>	768	</pre></div></div>
760	</div>	769	</div>
761	<div·class="nboutput·docutils·container">
762	<div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[9]:
763	</pre></div>
764	</div>
765	<div·class="output_area·docutils·container">
766	<div·class="highlight"><pre>
767	<matplotlib.legend.Legend·at·0xadde5de1e8ed>
768	</pre></div></div>
769	</div>
770	<div·class="nboutput·nblast·docutils·container">	770	<div·class="nboutput·nblast·docutils·container">
771	<div·class="prompt·empty·docutils·container">	771	<div·class="prompt·empty·docutils·container">
772	</div>	772	</div>
773	<div·class="output_area·docutils·container">	773	<div·class="output_area·docutils·container">
774	<img·alt="../../../_images/examples_notebooks_generated_ets_14_2.png"·src="../../../_images/examples_notebooks_generated_ets_14_2.png"·/>	774	<img·alt="../../../_images/examples_notebooks_generated_ets_14_2.png"·src="../../../_images/examples_notebooks_generated_ets_14_2.png"·/>
775	</div>	775	</div>
776	</div>	776	</div>


Offset 402, 14 lines modified		Offset 402, 16 lines modified

402	austourists.plot(label="data")	402	austourists.plot(label="data")
403	plt.ylabel("Australian·Tourists")	403	plt.ylabel("Australian·Tourists")

404	fit.fittedvalues.plot(label="statsmodels·fit")	404	fit.fittedvalues.plot(label="statsmodels·fit")
405	fit_R.fittedvalues.plot(label="R·fit",·linestyle="--")	405	fit_R.fittedvalues.plot(label="R·fit",·linestyle="--")
406	plt.legend()	406	plt.legend()
		407	[9]:
		408	<matplotlib.legend.Legend·at·0xadde5de1e8ed>
407	RUNNING·THE·L-BFGS-B·CODE	409	RUNNING·THE·L-BFGS-B·CODE

408	·············*	410	·············*

409	Machine·precision·=·2.220D-16	411	Machine·precision·=·2.220D-16
410	·N·=············9·····M·=···········10	412	·N·=············9·····M·=···········10

Offset 596, 16 lines modified		Offset 598, 14 lines modified
596	·············*	598	·············*

597	···N····Tit·····Tnf··Tnint··Skip··Nact·····Projg········F	599	···N····Tit·····Tnf··Tnint··Skip··Nact·····Projg········F
598	····9·····82····102·····90·····0·····1···1.643D-05···2.245D+00	600	····9·····82····102·····90·····0·····1···1.643D-05···2.245D+00
599	··F·=···2.2445124982934956	601	··F·=···2.2445124982934956

600	CONVERGENCE:·REL_REDUCTION_OF_F_<=_FACTR*EPSMCH	602	CONVERGENCE:·REL_REDUCTION_OF_F_<=_FACTR*EPSMCH
601	[9]:
602	<matplotlib.legend.Legend·at·0xadde5de1e8ed>
603	[../../../_images/examples_notebooks_generated_ets_14_2.png]	603	[../../../_images/examples_notebooks_generated_ets_14_2.png]
604	[10]:	604	[10]:
605	print(fit.summary())	605	print(fit.summary())
606	·································ETS·Results	606	·································ETS·Results
607	==============================================================================	607	==============================================================================
608	Dep.·Variable:······················y···No.·Observations:···················68	608	Dep.·Variable:······················y···No.·Observations:···················68
609	Model:······················ETS(AAdA)···Log·Likelihood················-152.627	609	Model:······················ETS(AAdA)···Log·Likelihood················-152.627


Offset 21, 18 lines modified		Offset 21, 18 lines modified
21	············]	21	············]
22	········},	22	········},
23	········{	23	········{
24	············"cell_type":·"code",	24	············"cell_type":·"code",
25	············"execution_count":·1,	25	············"execution_count":·1,
26	············"metadata":·{	26	············"metadata":·{
27	················"execution":·{	27	················"execution":·{
28	····················"iopub.execute_input":·"2025-12-09T22:22:41.~~750395~~Z",	28	····················"iopub.execute_input":·"2024-11-06T18:38:50.177440Z",
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30	····················"iopub.status.idle":·"2025-12-09T22:22:46.326~~187~~Z",	30	····················"iopub.status.idle":·"2024-11-06T18:38:53.026812Z",
31	····················"shell.execute_reply":·"2025-12-09T22:22:46.32~~5462~~Z"	31	····················"shell.execute_reply":·"2024-11-06T18:38:53.022258Z"
32	················}	32	················}
33	············},	33	············},
34	············"outputs":·[],	34	············"outputs":·[],
35	············"source":·[	35	············"source":·[
36	················"import·numpy·as·np\n",	36	················"import·numpy·as·np\n",
37	················"import·matplotlib.pyplot·as·plt\n",	37	················"import·matplotlib.pyplot·as·plt\n",
38	················"import·pandas·as·pd\n",	38	················"import·pandas·as·pd\n",
Offset 43, 18 lines modified		Offset 43, 18 lines modified
43	············]	43	············]
44	········},	44	········},
45	········{	45	········{
46	············"cell_type":·"code",	46	············"cell_type":·"code",
47	············"execution_count":·2,	47	············"execution_count":·2,
48	············"metadata":·{	48	············"metadata":·{
49	················"execution":·{	49	················"execution":·{
50	····················"iopub.execute_input":·"2025-12-09T22:22:46.~~342580~~Z",	50	····················"iopub.execute_input":·"2024-11-06T18:38:53.035444Z",
51	····················"iopub.status.busy":·"2025-12-09T22:22:46.342188Z",	51	····················"iopub.status.busy":·"2024-11-06T18:38:53.035018Z",
52	····················"iopub.status.idle":·"2025-12-09T22:22:46.350~~170~~Z",	52	····················"iopub.status.idle":·"2024-11-06T18:38:53.050991Z",
53	····················"shell.execute_reply":·"2025-12-09T22:22:46.~~349459~~Z"	53	····················"shell.execute_reply":·"2024-11-06T18:38:53.050247Z"
54	················}	54	················}
55	············},	55	············},
56	············"outputs":·[],	56	············"outputs":·[],
57	············"source":·[	57	············"source":·[
58	················"plt.rcParams[\"figure.figsize\"]·=·(12,·8)"	58	················"plt.rcParams[\"figure.figsize\"]·=·(12,·8)"
59	············]	59	············]
60	········},	60	········},
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82	············]	82	············]
83	········},	83	········},
84	········{	84	········{
85	············"cell_type":·"code",	85	············"cell_type":·"code",
86	············"execution_count":·3,	86	············"execution_count":·3,
87	············"metadata":·{	87	············"metadata":·{
88	················"execution":·{	88	················"execution":·{
89	····················"iopub.execute_input":·"2025-12-09T22:22:46.356261Z",	89	····················"iopub.execute_input":·"2024-11-06T18:38:53.059287Z",
90	····················"iopub.status.busy":·"2025-12-09T22:22:46.355978Z",	90	····················"iopub.status.busy":·"2024-11-06T18:38:53.058996Z",
91	····················"iopub.status.idle":·"2025-12-09T22:22:47.~~178170~~Z",	91	····················"iopub.status.idle":·"2024-11-06T18:38:53.590965Z",
92	····················"shell.execute_reply":·"2025-12-09T22:22:47.~~177453~~Z"	92	····················"shell.execute_reply":·"2024-11-06T18:38:53.590238Z"
93	················}	93	················}
94	············},	94	············},
95	············"outputs":·[	95	············"outputs":·[
96	················{	96	················{
97	····················"data":·{	97	····················"data":·{
98	························"text/plain":·[	98	························"text/plain":·[
99	····························"Text(0,·0.5,·'Annual·oil·production·in·Saudi·Arabia·(Mt)')"	99	····························"Text(0,·0.5,·'Annual·oil·production·in·Saudi·Arabia·(Mt)')"
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180	············]	180	············]
181	········},	181	········},
182	········{	182	········{
183	············"cell_type":·"code",	183	············"cell_type":·"code",
184	············"execution_count":·4,	184	············"execution_count":·4,
185	············"metadata":·{	185	············"metadata":·{
186	················"execution":·{	186	················"execution":·{
187	····················"iopub.execute_input":·"2025-12-09T22:22:47.198487Z",	187	····················"iopub.execute_input":·"2024-11-06T18:38:53.594851Z",
188	····················"iopub.status.busy":·"2025-12-09T22:22:47.19~~8213~~Z",	188	····················"iopub.status.busy":·"2024-11-06T18:38:53.594538Z",
189	····················"iopub.status.idle":·"2025-12-09T22:22:48.~~226191~~Z",	189	····················"iopub.status.idle":·"2024-11-06T18:38:54.042982Z",
190	····················"shell.execute_reply":·"2025-12-09T22:22:48.~~2254~~48Z"	190	····················"shell.execute_reply":·"2024-11-06T18:38:54.042247Z"
191	················}	191	················}
192	············},	192	············},
193	············"outputs":·[	193	············"outputs":·[
194	················{	194	················{
195	····················"name":·"stdout",	195	····················"name":·"stdout",
196	····················"output_type":·"stream",	196	····················"output_type":·"stream",
197	····················"text":·[	197	····················"text":·[
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278	········},	278	········},
279	········{	279	········{
280	············"cell_type":·"code",	280	············"cell_type":·"code",
281	············"execution_count":·5,	281	············"execution_count":·5,
282	············"metadata":·{	282	············"metadata":·{
283	················"execution":·{	283	················"execution":·{
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286	····················"iopub.status.idle":·"2025-12-09T22:22:49.~~218191~~Z",	286	····················"iopub.status.idle":·"2024-11-06T18:38:54.451000Z",
287	····················"shell.execute_reply":·"2025-12-09T22:22:49.~~217460~~Z"	287	····················"shell.execute_reply":·"2024-11-06T18:38:54.450207Z"
288	················}	288	················}
289	············},	289	············},
290	············"outputs":·[	290	············"outputs":·[
291	················{	291	················{
292	····················"name":·"stdout",	292	····················"name":·"stdout",
293	····················"output_type":·"stream",	293	····················"output_type":·"stream",
294	····················"text":·[	294	····················"text":·[
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370	········},	370	········},
371	········{	371	········{
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374	············"metadata":·{	374	············"metadata":·{
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379	····················"shell.execute_reply":·"2025-12-09T22:22:4~~9.33~~3603Z"	379	····················"shell.execute_reply":·"2024-11-06T18:38:54.502365Z"
380	················}	380	················}
381	············},	381	············},
382	············"outputs":·[	382	············"outputs":·[
383	················{	383	················{
384	····················"name":·"stdout",	384	····················"name":·"stdout",
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189	</div>	189	</div>
190	</div>	190	</div>
191	<div·class="nboutput·nblast·docutils·container">	191	<div·class="nboutput·nblast·docutils·container">
192	<div·class="prompt·empty·docutils·container">	192	<div·class="prompt·empty·docutils·container">
193	</div>	193	</div>
194	<div·class="output_area·stderr·docutils·container">	194	<div·class="output_area·stderr·docutils·container">
195	<div·class="highlight"><pre>	195	<div·class="highlight"><pre>
196	/tmp/ipykernel_28~~90636~~/3508103541.py:24:·FutureWarning:·'Y'·is·deprecated·and·will·be·removed·in·a·future·version,·please·use·'YE'·instead.	196	/tmp/ipykernel_2811274/3508103541.py:24:·FutureWarning:·'Y'·is·deprecated·and·will·be·removed·in·a·future·version,·please·use·'YE'·instead.
197	··index·=·pd.date_range(start="1996",·end="2008",·freq="Y")	197	··index·=·pd.date_range(start="1996",·end="2008",·freq="Y")
198	/tmp/ipykernel_28~~90636~~/3508103541.py:44:·FutureWarning:·'Y'·is·deprecated·and·will·be·removed·in·a·future·version,·please·use·'YE'·instead.	198	/tmp/ipykernel_2811274/3508103541.py:44:·FutureWarning:·'Y'·is·deprecated·and·will·be·removed·in·a·future·version,·please·use·'YE'·instead.
199	··index·=·pd.date_range(start="1990",·end="2005",·freq="Y")	199	··index·=·pd.date_range(start="1990",·end="2005",·freq="Y")
200	/tmp/ipykernel_28~~90636~~/3508103541.py:80:·FutureWarning:·'Y'·is·deprecated·and·will·be·removed·in·a·future·version,·please·use·'YE'·instead.	200	/tmp/ipykernel_2811274/3508103541.py:80:·FutureWarning:·'Y'·is·deprecated·and·will·be·removed·in·a·future·version,·please·use·'YE'·instead.
201	··index·=·pd.date_range(start="1970",·end="2001",·freq="Y")	201	··index·=·pd.date_range(start="1970",·end="2001",·freq="Y")
202	/tmp/ipykernel_28~~90636~~/3508103541.py:84:·FutureWarning:·'Y'·is·deprecated·and·will·be·removed·in·a·future·version,·please·use·'YE'·instead.	202	/tmp/ipykernel_2811274/3508103541.py:84:·FutureWarning:·'Y'·is·deprecated·and·will·be·removed·in·a·future·version,·please·use·'YE'·instead.
203	··index·=·pd.date_range(start="2001",·end="2008",·freq="Y")	203	··index·=·pd.date_range(start="2001",·end="2008",·freq="Y")
204	</pre></div></div>	204	</pre></div></div>
205	</div>	205	</div>
206	</section>	206	</section>
207	<section·id="Simple-Exponential-Smoothing">	207	<section·id="Simple-Exponential-Smoothing">
208	<h2>Simple·Exponential·Smoothing<a·class="headerlink"·href="#Simple-Exponential-Smoothing"·title="Link·to·this·heading">¶</a></h2>	208	<h2>Simple·Exponential·Smoothing<a·class="headerlink"·href="#Simple-Exponential-Smoothing"·title="Link·to·this·heading">¶</a></h2>
209	<p>Lets·use·Simple·Exponential·Smoothing·to·forecast·the·below·oil·data.</p>	209	<p>Lets·use·Simple·Exponential·Smoothing·to·forecast·the·below·oil·data.</p>


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230	······<th></th>	230	······<th></th>
231	······<th>Variance</th>	231	······<th>Variance</th>
232	····</tr>	232	····</tr>
233	··</thead>	233	··</thead>
234	··<tbody>	234	··<tbody>
235	····<tr>	235	····<tr>
236	······<th>groups_ix</th>	236	······<th>groups_ix</th>
237	······<td>0.~~888877~~</td>	237	······<td>1.062066</td>
238	····</tr>	238	····</tr>
239	····<tr>	239	····<tr>
240	······<th>level1_ix</th>	240	······<th>level1_ix</th>
241	······<td>2.~~134667~~</td>	241	······<td>1.985185</td>
242	····</tr>	242	····</tr>
243	····<tr>	243	····<tr>
244	······<th>level2_ix</th>	244	······<th>level2_ix</th>
245	······<td>2.~~973123~~</td>	245	······<td>3.025055</td>
246	····</tr>	246	····</tr>
247	····<tr>	247	····<tr>
248	······<th>Residual</th>	248	······<th>Residual</th>
249	······<td>3.~~97748~~5</td>	249	······<td>4.006615</td>
250	····</tr>	250	····</tr>
251	··</tbody>	251	··</tbody>
252	</table>	252	</table>
253	</div></div>	253	</div></div>
254	</div>	254	</div>
255	</section>	255	</section>


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79	The·estimated·covariance·parameters·should·be·similar·to·groups_var,	79	The·estimated·covariance·parameters·should·be·similar·to·groups_var,
80	level1_var,·etc.·as·defined·above.	80	level1_var,·etc.·as·defined·above.
81	[13]:	81	[13]:
82	r.cov_struct.summary()	82	r.cov_struct.summary()
83	[13]:	83	[13]:
84	·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·	84	·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·
85	\|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8\|_\x8V\x8V_\x8a\x8a_\x8r\x8r_\x8i\x8i_\x8a\x8a_\x8n\x8n_\x8c\x8c_\x8e\x8e\|	85	\|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8\|_\x8V\x8V_\x8a\x8a_\x8r\x8r_\x8i\x8i_\x8a\x8a_\x8n\x8n_\x8c\x8c_\x8e\x8e\|
86	\|_\x8g\x8g_\x8r\x8r_\x8o\x8o_\x8u\x8u_\x8p\x8p_\x8s\x8s_\x8_\x8__\x8i\x8i_\x8x\x8x_\x8\|_\x80_.._.8_.8_.8_.8_.7_.7\|	86	\|_\x8g\x8g_\x8r\x8r_\x8o\x8o_\x8u\x8u_\x8p\x8p_\x8s\x8s_\x8_\x8__\x8i\x8i_\x8x\x8x_\x8\|_\x81_.._.0_.6_.2_.0_.6_.6\|
87	\|_\x8l\x8l_\x8e\x8e_\x8v\x8v_\x8e\x8e_\x8l\x8l_\x81\x81_\x8_\x8__\x8i\x8i_\x8x\x8x_\x8\|_\x82_\x8._\x81_\x83_\x84_\x86_\x86_\x87\|
88	\|_\x8l\x8l_\x8e\x8e_\x8v\x8v_\x8e\x8e_\x8l\x8l_\x82.2_._.__.i.i_.x.x_.\|_.2_.._.9_.7_.3_.1_.2_.3\|	87	\|_\x8l\x8l_\x8e\x8e_\x8v\x8v_\x8e\x8e_\x8l\x8l_\x81.1_._.__.i.i_.x.x_.\|_.1_.._.9_.8_.5_.1_.8_.5\|
		88	\|_\x8l\x8l_\x8e\x8e_\x8v\x8v_\x8e\x8e_\x8l\x8l_\x82\x82_\x8_\x8__\x8i\x8i_\x8x\x8x_\x8\|_\x83_\x8._\x80_\x82_\x85_\x80_\x85_\x85\|
89	\|_\x8R\x8R_\x8e\x8e_\x8s\x8s_\x8i\x8i_\x8d\x8d_\x8u\x8u_\x8a\x8a_\x8l\x8l_\x8·_\x8\|_\x83_.._.9_.7_.7_.4_.8_\x85\|	89	\|_\x8R\x8R_\x8e\x8e_\x8s\x8s_\x8i\x8i_\x8d\x8d_\x8u\x8u_\x8a\x8a_\x8l\x8l_\x8·_\x8\|_\x84_.._.0_.0_.6_.6_.1_\x85\|
90	_\x8[_\x8L_\x8o_\x8g_\x8o_\x8·_\x8o_\x8f_\x8·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x84_\x8+_\x8d_\x8f_\x8s_\x8g_\x8]	90	_\x8[_\x8L_\x8o_\x8g_\x8o_\x8·_\x8o_\x8f_\x8·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x84_\x8+_\x8d_\x8f_\x8s_\x8g_\x8]
91	\x8\x8\x8\x8·_\x8T\x8T_\x8a\x8a_\x8b\x8b_\x8l\x8l_\x8e\x8e_\x8·_\x8o\x8o_\x8f\x8f_\x8·_\x8C\x8C_\x8o\x8o_\x8n\x8n_\x8t\x8t_\x8e\x8e_\x8n\x8n_\x8t\x8t_\x8s\x8s·\x8\x8\x8\x8	91	\x8\x8\x8\x8·_\x8T\x8T_\x8a\x8a_\x8b\x8b_\x8l\x8l_\x8e\x8e_\x8·_\x8o\x8o_\x8f\x8f_\x8·_\x8C\x8C_\x8o\x8o_\x8n\x8n_\x8t\x8t_\x8e\x8e_\x8n\x8n_\x8t\x8t_\x8s\x8s·\x8\x8\x8\x8
92	····*·_\x8I_\x8n_\x8s_\x8t_\x8a_\x8l_\x8l_\x8i_\x8n_\x8g_\x8·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s	92	····*·_\x8I_\x8n_\x8s_\x8t_\x8a_\x8l_\x8l_\x8i_\x8n_\x8g_\x8·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s
93	····*·_\x8G_\x8e_\x8t_\x8t_\x8i_\x8n_\x8g_\x8·_\x8s_\x8t_\x8a_\x8r_\x8t_\x8e_\x8d	93	····*·_\x8G_\x8e_\x8t_\x8t_\x8i_\x8n_\x8g_\x8·_\x8s_\x8t_\x8a_\x8r_\x8t_\x8e_\x8d
94	····*·_\x8U_\x8s_\x8e_\x8r_\x8·_\x8G_\x8u_\x8i_\x8d_\x8e	94	····*·_\x8U_\x8s_\x8e_\x8r_\x8·_\x8G_\x8u_\x8i_\x8d_\x8e
95	····*·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s	95	····*·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s
96	····*·_\x8A_\x8P_\x8I_\x8·_\x8R_\x8e_\x8f_\x8e_\x8r_\x8e_\x8n_\x8c_\x8e	96	····*·_\x8A_\x8P_\x8I_\x8·_\x8R_\x8e_\x8f_\x8e_\x8r_\x8e_\x8n_\x8c_\x8e


Offset 126, 24 lines modified		Offset 126, 24 lines modified
126	····59.7668,	126	····59.7668,
127	····35.1919,	127	····35.1919,
128	····44.3197,	128	····44.3197,
129	····47.9137,	129	····47.9137,
130	]	130	]
131	index·=·pd.date_range(start="2005",·end="2010-Q4",·freq="QS-OCT")	131	index·=·pd.date_range(start="2005",·end="2010-Q4",·freq="QS-OCT")
132	aust·=·pd.Series(data,·index)	132	aust·=·pd.Series(data,·index)
133	/tmp/ipykernel_28~~90636~~/3508103541.py:24:·FutureWarning:·'Y'·is·deprecated·and	133	/tmp/ipykernel_2811274/3508103541.py:24:·FutureWarning:·'Y'·is·deprecated·and
134	will·be·removed·in·a·future·version,·please·use·'YE'·instead.	134	will·be·removed·in·a·future·version,·please·use·'YE'·instead.
135	··index·=·pd.date_range(start="1996",·end="2008",·freq="Y")	135	··index·=·pd.date_range(start="1996",·end="2008",·freq="Y")
136	/tmp/ipykernel_28~~90636~~/3508103541.py:44:·FutureWarning:·'Y'·is·deprecated·and	136	/tmp/ipykernel_2811274/3508103541.py:44:·FutureWarning:·'Y'·is·deprecated·and
137	will·be·removed·in·a·future·version,·please·use·'YE'·instead.	137	will·be·removed·in·a·future·version,·please·use·'YE'·instead.
138	··index·=·pd.date_range(start="1990",·end="2005",·freq="Y")	138	··index·=·pd.date_range(start="1990",·end="2005",·freq="Y")
139	/tmp/ipykernel_28~~90636~~/3508103541.py:80:·FutureWarning:·'Y'·is·deprecated·and	139	/tmp/ipykernel_2811274/3508103541.py:80:·FutureWarning:·'Y'·is·deprecated·and
140	will·be·removed·in·a·future·version,·please·use·'YE'·instead.	140	will·be·removed·in·a·future·version,·please·use·'YE'·instead.
141	··index·=·pd.date_range(start="1970",·end="2001",·freq="Y")	141	··index·=·pd.date_range(start="1970",·end="2001",·freq="Y")
142	/tmp/ipykernel_28~~90636~~/3508103541.py:84:·FutureWarning:·'Y'·is·deprecated·and	142	/tmp/ipykernel_2811274/3508103541.py:84:·FutureWarning:·'Y'·is·deprecated·and
143	will·be·removed·in·a·future·version,·please·use·'YE'·instead.	143	will·be·removed·in·a·future·version,·please·use·'YE'·instead.
144	··index·=·pd.date_range(start="2001",·end="2008",·freq="Y")	144	··index·=·pd.date_range(start="2001",·end="2008",·freq="Y")
145	\x8\x8\x8\x8\x8·S\x8Si\x8im\x8mp\x8pl\x8le\x8e·E\x8Ex\x8xp\x8po\x8on\x8ne\x8en\x8nt\x8ti\x8ia\x8al\x8l·S\x8Sm\x8mo\x8oo\x8ot\x8th\x8hi\x8in\x8ng\x8g_\x8?\x8¶·\x8\x8\x8\x8\x8	145	\x8\x8\x8\x8\x8·S\x8Si\x8im\x8mp\x8pl\x8le\x8e·E\x8Ex\x8xp\x8po\x8on\x8ne\x8en\x8nt\x8ti\x8ia\x8al\x8l·S\x8Sm\x8mo\x8oo\x8ot\x8th\x8hi\x8in\x8ng\x8g_\x8?\x8¶·\x8\x8\x8\x8\x8
146	Lets·use·Simple·Exponential·Smoothing·to·forecast·the·below·oil·data.	146	Lets·use·Simple·Exponential·Smoothing·to·forecast·the·below·oil·data.
147	[2]:	147	[2]:
148	ax·=·oildata.plot()	148	ax·=·oildata.plot()
149	ax.set_xlabel("Year")	149	ax.set_xlabel("Year")


Offset 12, 18 lines modified		Offset 12, 18 lines modified
12	············]	12	············]
13	········},	13	········},
14	········{	14	········{
15	············"cell_type":·"code",	15	············"cell_type":·"code",
16	············"execution_count":·1,	16	············"execution_count":·1,
17	············"metadata":·{	17	············"metadata":·{
18	················"execution":·{	18	················"execution":·{
19	····················"iopub.execute_input":·"2025-12-09T22:24:20.~~942365~~Z",	19	····················"iopub.execute_input":·"2024-11-06T18:40:28.631478Z",
20	····················"iopub.status.busy":·"2025-12-09T22:24:20.~~942~~104Z",	20	····················"iopub.status.busy":·"2024-11-06T18:40:28.631166Z",
21	····················"iopub.status.idle":·"2025-12-09T22:24:24.~~7540~~56Z",	21	····················"iopub.status.idle":·"2024-11-06T18:40:32.097450Z",
22	····················"shell.execute_reply":·"2025-12-09T22:24:24.~~753436~~Z"	22	····················"shell.execute_reply":·"2024-11-06T18:40:32.096677Z"
23	················}	23	················}
24	············},	24	············},
25	············"outputs":·[],	25	············"outputs":·[],
26	············"source":·[	26	············"source":·[
27	················"import·numpy·as·np\n",	27	················"import·numpy·as·np\n",
28	················"import·pandas·as·pd\n",	28	················"import·pandas·as·pd\n",
29	················"import·statsmodels.api·as·sm"	29	················"import·statsmodels.api·as·sm"
Offset 37, 18 lines modified		Offset 37, 18 lines modified
37	············]	37	············]
38	········},	38	········},
39	········{	39	········{
40	············"cell_type":·"code",	40	············"cell_type":·"code",
41	············"execution_count":·2,	41	············"execution_count":·2,
42	············"metadata":·{	42	············"metadata":·{
43	················"execution":·{	43	················"execution":·{
44	····················"iopub.execute_input":·"2025-12-09T22:24:24.~~762536~~Z",	44	····················"iopub.execute_input":·"2024-11-06T18:40:32.111443Z",
45	····················"iopub.status.busy":·"2025-12-09T22:24:24.762151Z",	45	····················"iopub.status.busy":·"2024-11-06T18:40:32.111013Z",
46	····················"iopub.status.idle":·"2025-12-09T22:24:24.~~7740~~86Z",	46	····················"iopub.status.idle":·"2024-11-06T18:40:32.122983Z",
47	····················"shell.execute_reply":·"2025-12-09T22:24:24.~~773463~~Z"	47	····················"shell.execute_reply":·"2024-11-06T18:40:32.122252Z"
48	················}	48	················}
49	············},	49	············},
50	············"outputs":·[],	50	············"outputs":·[],
51	············"source":·[	51	············"source":·[
52	················"p·=·5"	52	················"p·=·5"
53	············]	53	············]
54	········},	54	········},
Offset 60, 18 lines modified		Offset 60, 18 lines modified
60	············]	60	············]
61	········},	61	········},
62	········{	62	········{
63	············"cell_type":·"code",	63	············"cell_type":·"code",
64	············"execution_count":·3,	64	············"execution_count":·3,
65	············"metadata":·{	65	············"metadata":·{
66	················"execution":·{	66	················"execution":·{
67	····················"iopub.execute_input":·"2025-12-09T22:24:24.~~780~~291Z",	67	····················"iopub.execute_input":·"2024-11-06T18:40:32.135262Z",
68	····················"iopub.status.busy":·"2025-12-09T22:24:24.~~780026~~Z",	68	····················"iopub.status.busy":·"2024-11-06T18:40:32.134972Z",
69	····················"iopub.status.idle":·"2025-12-09T22:24:24.~~794~~072Z",	69	····················"iopub.status.idle":·"2024-11-06T18:40:32.147085Z",
70	····················"shell.execute_reply":·"2025-12-09T22:24:24.~~793439~~Z"	70	····················"shell.execute_reply":·"2024-11-06T18:40:32.146350Z"
71	················}	71	················}
72	············},	72	············},
73	············"outputs":·[],	73	············"outputs":·[],
74	············"source":·[	74	············"source":·[
75	················"groups_var·=·1\n",	75	················"groups_var·=·1\n",
76	················"level1_var·=·2\n",	76	················"level1_var·=·2\n",
77	················"level2_var·=·3\n",	77	················"level2_var·=·3\n",
Offset 86, 18 lines modified		Offset 86, 18 lines modified
86	············]	86	············]
87	········},	87	········},
88	········{	88	········{
89	············"cell_type":·"code",	89	············"cell_type":·"code",
90	············"execution_count":·4,	90	············"execution_count":·4,
91	············"metadata":·{	91	············"metadata":·{
92	················"execution":·{	92	················"execution":·{
93	····················"iopub.execute_input":·"2025-12-09T22:24:24.~~8023~~52Z",	93	····················"iopub.execute_input":·"2024-11-06T18:40:32.155256Z",
94	····················"iopub.status.busy":·"2025-12-09T22:24:24.~~802092~~Z",	94	····················"iopub.status.busy":·"2024-11-06T18:40:32.154967Z",
95	····················"iopub.status.idle":·"2025-12-09T22:24:24.~~810~~225Z",	95	····················"iopub.status.idle":·"2024-11-06T18:40:32.163243Z",
96	····················"shell.execute_reply":·"2025-12-09T22:24:24.~~809~~596Z"	96	····················"shell.execute_reply":·"2024-11-06T18:40:32.162512Z"
97	················}	97	················}
98	············},	98	············},
99	············"outputs":·[],	99	············"outputs":·[],
100	············"source":·[	100	············"source":·[
101	················"n_groups·=·100"	101	················"n_groups·=·100"
102	············]	102	············]
103	········},	103	········},
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109	············]	109	············]
110	········},	110	········},
111	········{	111	········{
112	············"cell_type":·"code",	112	············"cell_type":·"code",
113	············"execution_count":·5,	113	············"execution_count":·5,
114	············"metadata":·{	114	············"metadata":·{
115	················"execution":·{	115	················"execution":·{
116	····················"iopub.execute_input":·"2025-12-09T22:24:24.816086Z",	116	····················"iopub.execute_input":·"2024-11-06T18:40:32.167482Z",
117	····················"iopub.status.busy":·"2025-12-09T22:24:24.815819Z",	117	····················"iopub.status.busy":·"2024-11-06T18:40:32.167196Z",
118	····················"iopub.status.idle":·"2025-12-09T22:24:24.826~~095~~Z",	118	····················"iopub.status.idle":·"2024-11-06T18:40:32.182974Z",
119	····················"shell.execute_reply":·"2025-12-09T22:24:24.825~~449~~Z"	119	····················"shell.execute_reply":·"2024-11-06T18:40:32.182261Z"
120	················}	120	················}
121	············},	121	············},
122	············"outputs":·[],	122	············"outputs":·[],
123	············"source":·[	123	············"source":·[
124	················"group_size·=·20\n",	124	················"group_size·=·20\n",
125	················"level1_size·=·10\n",	125	················"level1_size·=·10\n",
126	················"level2_size·=·5"	126	················"level2_size·=·5"
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134	············]	134	············]
135	········},	135	········},
136	········{	136	········{
137	············"cell_type":·"code",	137	············"cell_type":·"code",
138	············"execution_count":·6,	138	············"execution_count":·6,
139	············"metadata":·{	139	············"metadata":·{
140	················"execution":·{	140	················"execution":·{
141	····················"iopub.execute_input":·"2025-12-09T22:24:24.~~830473~~Z",	141	····················"iopub.execute_input":·"2024-11-06T18:40:32.186912Z",
142	····················"iopub.status.busy":·"2025-12-09T22:24:24.830212Z",	142	····················"iopub.status.busy":·"2024-11-06T18:40:32.186621Z",
143	····················"iopub.status.idle":·"2025-12-09T22:24:24.~~842~~097Z",	143	····················"iopub.status.idle":·"2024-11-06T18:40:32.197030Z",
144	····················"shell.execute_reply":·"2025-12-09T22:24:24.~~841440~~Z"	144	····················"shell.execute_reply":·"2024-11-06T18:40:32.196333Z"
145	················}	145	················}
146	············},	146	············},
147	············"outputs":·[],	147	············"outputs":·[],
148	············"source":·[	148	············"source":·[
149	················"n·=·n_groups··group_size··level1_size·*·level2_size"	149	················"n·=·n_groups··group_size··level1_size·*·level2_size"
150	············]	150	············]
151	········},	151	········},
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157	············]	157	············]
158	········},	158	········},
159	········{	159	········{
160	············"cell_type":·"code",	160	············"cell_type":·"code",
161	············"execution_count":·7,	161	············"execution_count":·7,
162	············"metadata":·{	162	············"metadata":·{
163	················"execution":·{	163	················"execution":·{
164	····················"iopub.execute_input":·"2025-12-09T22:24:24.~~845~~675Z",	164	····················"iopub.execute_input":·"2024-11-06T18:40:32.200609Z",
165	····················"iopub.status.busy":·"2025-12-09T22:24:24.~~8453~~98Z",	165	····················"iopub.status.busy":·"2024-11-06T18:40:32.200299Z",
166	····················"iopub.status.idle":·"2025-12-09T22:24:24.~~9181~~25Z",	166	····················"iopub.status.idle":·"2024-11-06T18:40:32.259025Z",
167	····················"shell.execute_reply":·"2025-12-09T22:24:24.~~9174~~50Z"	167	····················"shell.execute_reply":·"2024-11-06T18:40:32.258252Z"
168	················}	168	················}
169	············},	169	············},
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14	············]	14	············]
15	········},	15	········},
16	········{	16	········{
17	············"cell_type":·"code",	17	············"cell_type":·"code",
18	············"execution_count":·1,	18	············"execution_count":·1,
19	············"metadata":·{	19	············"metadata":·{
20	················"execution":·{	20	················"execution":·{
21	····················"iopub.execute_input":·"2025-12-09T22:22:41.~~766~~461Z",	21	····················"iopub.execute_input":·"2024-11-06T18:38:50.685452Z",
22	····················"iopub.status.busy":·"2025-12-09T22:22:41.~~766~~196Z",	22	····················"iopub.status.busy":·"2024-11-06T18:38:50.685174Z",
23	····················"iopub.status.idle":·"2025-12-09T22:22:46.~~99814~~6Z",	23	····················"iopub.status.idle":·"2024-11-06T18:38:52.763036Z",
24	····················"shell.execute_reply":·"2025-12-09T22:22:46.~~997431~~Z"	24	····················"shell.execute_reply":·"2024-11-06T18:38:52.762260Z"
25	················}	25	················}
26	············},	26	············},
27	············"outputs":·[],	27	············"outputs":·[],
28	············"source":·[	28	············"source":·[
29	················"import·pandas·as·pd\n",	29	················"import·pandas·as·pd\n",
30	················"import·numpy·as·np\n",	30	················"import·numpy·as·np\n",
31	················"from·scipy.stats.distributions·import·norm,·poisson\n",	31	················"from·scipy.stats.distributions·import·norm,·poisson\n",
Offset 42, 18 lines modified		Offset 42, 18 lines modified
42	············]	42	············]
43	········},	43	········},
44	········{	44	········{
45	············"cell_type":·"code",	45	············"cell_type":·"code",
46	············"execution_count":·2,	46	············"execution_count":·2,
47	············"metadata":·{	47	············"metadata":·{
48	················"execution":·{	48	················"execution":·{
49	····················"iopub.execute_input":·"2025-12-09T22:22:47.004248Z",	49	····················"iopub.execute_input":·"2024-11-06T18:38:52.770094Z",
50	····················"iopub.status.busy":·"2025-12-09T22:22:47.~~001951~~Z",	50	····················"iopub.status.busy":·"2024-11-06T18:38:52.767538Z",
51	····················"iopub.status.idle":·"2025-12-09T22:22:47.~~02619~~3Z",	51	····················"iopub.status.idle":·"2024-11-06T18:38:52.782273Z",
52	····················"shell.execute_reply":·"2025-12-09T22:22:47.~~025464~~Z"	52	····················"shell.execute_reply":·"2024-11-06T18:38:52.781229Z"
53	················},	53	················},
54	················"lines_to_next_cell":·1	54	················"lines_to_next_cell":·1
55	············},	55	············},
56	············"outputs":·[],	56	············"outputs":·[],
57	············"source":·[	57	············"source":·[
58	················"def·negbinom(u,·mu,·scale):\n",	58	················"def·negbinom(u,·mu,·scale):\n",
59	················"····p·=·(scale·-·1)·/·scale\n",	59	················"····p·=·(scale·-·1)·/·scale\n",
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70	············]	70	············]
71	········},	71	········},
72	········{	72	········{
73	············"cell_type":·"code",	73	············"cell_type":·"code",
74	············"execution_count":·3,	74	············"execution_count":·3,
75	············"metadata":·{	75	············"metadata":·{
76	················"execution":·{	76	················"execution":·{
77	····················"iopub.execute_input":·"2025-12-09T22:22:47.~~029924~~Z",	77	····················"iopub.execute_input":·"2024-11-06T18:38:52.786415Z",
78	····················"iopub.status.busy":·"2025-12-09T22:22:47.~~0296~~19Z",	78	····················"iopub.status.busy":·"2024-11-06T18:38:52.786113Z",
79	····················"iopub.status.idle":·"2025-12-09T22:22:47.~~046162~~Z",	79	····················"iopub.status.idle":·"2024-11-06T18:38:52.791798Z",
80	····················"shell.execute_reply":·"2025-12-09T22:22:47.~~045457~~Z"	80	····················"shell.execute_reply":·"2024-11-06T18:38:52.791125Z"
81	················}	81	················}
82	············},	82	············},
83	············"outputs":·[],	83	············"outputs":·[],
84	············"source":·[	84	············"source":·[
85	················"#·Sample·size\n",	85	················"#·Sample·size\n",
86	················"n·=·1000\n",	86	················"n·=·1000\n",
87	················"\n",	87	················"\n",
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106	············]	106	············]
107	········},	107	········},
108	········{	108	········{
109	············"cell_type":·"code",	109	············"cell_type":·"code",
110	············"execution_count":·4,	110	············"execution_count":·4,
111	············"metadata":·{	111	············"metadata":·{
112	················"execution":·{	112	················"execution":·{
113	····················"iopub.execute_input":·"2025-12-09T22:22:47.~~049925~~Z",	113	····················"iopub.execute_input":·"2024-11-06T18:38:52.795604Z",
114	····················"iopub.status.busy":·"2025-12-09T22:22:47.~~0496~~08Z",	114	····················"iopub.status.busy":·"2024-11-06T18:38:52.795306Z",
115	····················"iopub.status.idle":·"2025-12-09T22:22:47.~~070165~~Z",	115	····················"iopub.status.idle":·"2024-11-06T18:38:52.806938Z",
116	····················"shell.execute_reply":·"2025-12-09T22:22:47.069~~454~~Z"	116	····················"shell.execute_reply":·"2024-11-06T18:38:52.806239Z"
117	················}	117	················}
118	············},	118	············},
119	············"outputs":·[],	119	············"outputs":·[],
120	············"source":·[	120	············"source":·[
121	················"#·Build·a·design·matrix·for·the·alternative·(more·complex)·model\n",	121	················"#·Build·a·design·matrix·for·the·alternative·(more·complex)·model\n",
122	················"x·=·np.random.normal(size=(n,·p))\n",	122	················"x·=·np.random.normal(size=(n,·p))\n",
123	················"x[:,·0]·=·1"	123	················"x[:,·0]·=·1"
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131	············]	131	············]
132	········},	132	········},
133	········{	133	········{
134	············"cell_type":·"code",	134	············"cell_type":·"code",
135	············"execution_count":·5,	135	············"execution_count":·5,
136	············"metadata":·{	136	············"metadata":·{
137	················"execution":·{	137	················"execution":·{
138	····················"iopub.execute_input":·"2025-12-09T22:22:47.~~073957~~Z",	138	····················"iopub.execute_input":·"2024-11-06T18:38:52.810608Z",
139	····················"iopub.status.busy":·"2025-12-09T22:22:47.~~073645~~Z",	139	····················"iopub.status.busy":·"2024-11-06T18:38:52.810328Z",
140	····················"iopub.status.idle":·"2025-12-09T22:22:47.~~090141~~Z",	140	····················"iopub.status.idle":·"2024-11-06T18:38:52.818970Z",
141	····················"shell.execute_reply":·"2025-12-09T22:22:47.089427Z"	141	····················"shell.execute_reply":·"2024-11-06T18:38:52.818239Z"
142	················}	142	················}
143	············},	143	············},
144	············"outputs":·[],	144	············"outputs":·[],
145	············"source":·[	145	············"source":·[
146	················"x0·=·x[:,·0:3]"	146	················"x0·=·x[:,·0:3]"
147	············]	147	············]
148	········},	148	········},
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154	············]	154	············]
155	········},	155	········},
156	········{	156	········{
157	············"cell_type":·"code",	157	············"cell_type":·"code",
158	············"execution_count":·6,	158	············"execution_count":·6,
159	············"metadata":·{	159	············"metadata":·{
160	················"execution":·{	160	················"execution":·{
161	····················"iopub.execute_input":·"2025-12-09T22:22:47.~~093889~~Z",	161	····················"iopub.execute_input":·"2024-11-06T18:38:52.822798Z",
162	····················"iopub.status.busy":·"2025-12-09T22:22:47.~~093~~587Z",	162	····················"iopub.status.busy":·"2024-11-06T18:38:52.822509Z",
163	····················"iopub.status.idle":·"2025-12-09T22:22:47.110~~177~~Z",	163	····················"iopub.status.idle":·"2024-11-06T18:38:52.830238Z",
164	····················"shell.execute_reply":·"2025-12-09T22:22:47.109~~455~~Z"	164	····················"shell.execute_reply":·"2024-11-06T18:38:52.829508Z"
165	················}	165	················}
166	············},	166	············},
167	············"outputs":·[],	167	············"outputs":·[],
168	············"source":·[	168	············"source":·[
169	················"#·Scale·parameter·for·negative·binomial·distribution\n",	169	················"#·Scale·parameter·for·negative·binomial·distribution\n",
170	················"scale·=·10"	170	················"scale·=·10"
171	············]	171	············]
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178	············]	178	············]
179	········},	179	········},
180	········{	180	········{
181	············"cell_type":·"code",	181	············"cell_type":·"code",
182	············"execution_count":·7,	182	············"execution_count":·7,
183	············"metadata":·{	183	············"metadata":·{
184	················"execution":·{	184	················"execution":·{
185	····················"iopub.execute_input":·"2025-12-09T22:22:47.113~~912~~Z",	185	····················"iopub.execute_input":·"2024-11-06T18:38:52.833630Z",
186	····················"iopub.status.busy":·"2025-12-09T22:22:47.113~~603~~Z",	186	····················"iopub.status.busy":·"2024-11-06T18:38:52.833344Z",
187	····················"iopub.status.idle":·"2025-12-09T22:22:47.~~122110~~Z",	187	····················"iopub.status.idle":·"2024-11-06T18:38:52.848931Z",
188	····················"shell.execute_reply":·"2025-12-09T22:22:47.~~12142~~6Z"	188	····················"shell.execute_reply":·"2024-11-06T18:38:52.848236Z"
189	················}	189	················}
190	············},	190	············},
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27	············]	27	············]
28	········},	28	········},
29	········{	29	········{
30	············"cell_type":·"code",	30	············"cell_type":·"code",
31	············"execution_count":·1,	31	············"execution_count":·1,
32	············"metadata":·{	32	············"metadata":·{
33	················"execution":·{	33	················"execution":·{
34	····················"iopub.execute_input":·"2025-12-09T22:22:41.~~886426~~Z",	34	····················"iopub.execute_input":·"2024-11-06T18:38:50.201777Z",
35	····················"iopub.status.busy":·"2025-12-09T22:22:41.~~886153~~Z",	35	····················"iopub.status.busy":·"2024-11-06T18:38:50.201491Z",
36	····················"iopub.status.idle":·"2025-12-09T22:22:45.40~~2255~~Z",	36	····················"iopub.status.idle":·"2024-11-06T18:38:52.505477Z",
37	····················"shell.execute_reply":·"2025-12-09T22:22:45.40~~146~~7Z"	37	····················"shell.execute_reply":·"2024-11-06T18:38:52.504747Z"
38	················},	38	················},
39	················"jupyter":·{	39	················"jupyter":·{
40	····················"outputs_hidden":·false	40	····················"outputs_hidden":·false
41	················}	41	················}
42	············},	42	············},
43	············"outputs":·[],	43	············"outputs":·[],
44	············"source":·[	44	············"source":·[
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56	············]	56	············]
57	········},	57	········},
58	········{	58	········{
59	············"cell_type":·"code",	59	············"cell_type":·"code",
60	············"execution_count":·2,	60	············"execution_count":·2,
61	············"metadata":·{	61	············"metadata":·{
62	················"execution":·{	62	················"execution":·{
63	····················"iopub.execute_input":·"2025-12-09T22:22:45.40~~8600~~Z",	63	····················"iopub.execute_input":·"2024-11-06T18:38:52.509846Z",
64	····················"iopub.status.busy":·"2025-12-09T22:22:45.40~~8200~~Z",	64	····················"iopub.status.busy":·"2024-11-06T18:38:52.509398Z",
65	····················"iopub.status.idle":·"2025-12-09T22:22:45.~~462209~~Z",	65	····················"iopub.status.idle":·"2024-11-06T18:38:52.550933Z",
66	····················"shell.execute_reply":·"2025-12-09T22:22:45.~~461448~~Z"	66	····················"shell.execute_reply":·"2024-11-06T18:38:52.550227Z"
67	················},	67	················},
68	················"jupyter":·{	68	················"jupyter":·{
69	····················"outputs_hidden":·false	69	····················"outputs_hidden":·false
70	················}	70	················}
71	············},	71	············},
72	············"outputs":·[	72	············"outputs":·[
73	················{	73	················{
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113	············]	113	············]
114	········},	114	········},
115	········{	115	········{
116	············"cell_type":·"code",	116	············"cell_type":·"code",
117	············"execution_count":·3,	117	············"execution_count":·3,
118	············"metadata":·{	118	············"metadata":·{
119	················"execution":·{	119	················"execution":·{
120	····················"iopub.execute_input":·"2025-12-09T22:22:45.56~~576~~0Z",	120	····················"iopub.execute_input":·"2024-11-06T18:38:52.623109Z",
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23	················"%matplotlib·inline"	23	················"%matplotlib·inline"
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39	················"import·numpy·as·np\n",	39	················"import·numpy·as·np\n",
40	················"import·statsmodels.api·as·sm\n",	40	················"import·statsmodels.api·as·sm\n",
41	················"from·scipy·import·stats\n",	41	················"from·scipy·import·stats\n",
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59	············]	59	············]
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143	················"data·=·sm.datasets.star98.load()\n",	143	················"data·=·sm.datasets.star98.load()\n",
144	················"data.exog·=·sm.add_constant(data.exog,·prepend=False)"	144	················"data.exog·=·sm.add_constant(data.exog,·prepend=False)"
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253	············"metadata":·{	253	············"metadata":·{
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255	····················"iopub.execute_input":·"2025-12-09T22:24:25.~~026393~~Z",	255	····················"iopub.execute_input":·"2024-11-06T18:40:33.831257Z",
256	····················"iopub.status.busy":·"2025-12-09T22:24:25.~~026114~~Z",	256	····················"iopub.status.busy":·"2024-11-06T18:40:33.830965Z",
257	····················"iopub.status.idle":·"2025-12-09T22:24:25.102~~103~~Z",	257	····················"iopub.status.idle":·"2024-11-06T18:40:33.902960Z",
258	····················"shell.execute_reply":·"2025-12-09T22:24:25.10~~1429~~Z"	258	····················"shell.execute_reply":·"2024-11-06T18:40:33.902243Z"
259	················}	259	················}
260	············},	260	············},
261	············"outputs":·[	261	············"outputs":·[
262	················{	262	················{
263	····················"name":·"stdout",	263	····················"name":·"stdout",
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Offset 230, 17 lines modified		Offset 230, 17 lines modified
230	</pre></div></div>	230	</pre></div></div>
231	</div>	231	</div>
232	<div·class="nboutput·nblast·docutils·container">	232	<div·class="nboutput·nblast·docutils·container">
233	<div·class="prompt·empty·docutils·container">	233	<div·class="prompt·empty·docutils·container">
234	</div>	234	</div>
235	<div·class="output_area·stderr·docutils·container">	235	<div·class="output_area·stderr·docutils·container">
236	<div·class="highlight"><pre>	236	<div·class="highlight"><pre>
237	/tmp/ipykernel_2897538/1000445862.py:1:·FutureWarning:·Series.__getitem__·treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by·position,·use·`ser.iloc[pos]`	237	/tmp/ipykernel_2844558/1000445862.py:1:·FutureWarning:·Series.__getitem__·treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by·position,·use·`ser.iloc[pos]`
238	··print(mod1.params[1])	238	··print(mod1.params[1])
239	/tmp/ipykernel_2897538/1000445862.py:2:·FutureWarning:·Series.__getitem__·treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by·position,·use·`ser.iloc[pos]`	239	/tmp/ipykernel_2844558/1000445862.py:2:·FutureWarning:·Series.__getitem__·treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by·position,·use·`ser.iloc[pos]`
240	··print(mod2.params[1]·*·2)	240	··print(mod2.params[1]·*·2)
241	</pre></div></div>	241	</pre></div></div>
242	</div>	242	</div>
243	</section>	243	</section>


244	············<div·class="clearer"></div>	244	············<div·class="clearer"></div>


Offset 176, 20 lines modified		Offset 176, 20 lines modified
176	As·expected,·the·coefficient·for·double_it(LOWINC)·in·the·second·model·is·half	176	As·expected,·the·coefficient·for·double_it(LOWINC)·in·the·second·model·is·half
177	the·size·of·the·LOWINC·coefficient·from·the·first·model:	177	the·size·of·the·LOWINC·coefficient·from·the·first·model:
178	[4]:	178	[4]:
179	print(mod1.params[1])	179	print(mod1.params[1])
180	print(mod2.params[1]·*·2)	180	print(mod2.params[1]·*·2)
181	-0.020395987154756403	181	-0.020395987154756403
182	-0.020395987154757343	182	-0.020395987154757343
183	/tmp/ipykernel_2897538/1000445862.py:1:·FutureWarning:·Series.__getitem__	183	/tmp/ipykernel_2844558/1000445862.py:1:·FutureWarning:·Series.__getitem__
184	treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys	184	treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys
185	will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To	185	will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To
186	access·a·value·by·position,·use·`ser.iloc[pos]`	186	access·a·value·by·position,·use·`ser.iloc[pos]`
187	··print(mod1.params[1])	187	··print(mod1.params[1])
188	/tmp/ipykernel_2897538/1000445862.py:2:·FutureWarning:·Series.__getitem__	188	/tmp/ipykernel_2844558/1000445862.py:2:·FutureWarning:·Series.__getitem__
189	treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys	189	treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys
190	will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To	190	will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To
191	access·a·value·by·position,·use·`ser.iloc[pos]`	191	access·a·value·by·position,·use·`ser.iloc[pos]`
192	··print(mod2.params[1]·*·2)	192	··print(mod2.params[1]·*·2)
193	_\x8[_\x8L_\x8o_\x8g_\x8o_\x8·_\x8o_\x8f_\x8·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x84_\x8+_\x8d_\x8f_\x8s_\x8g_\x8]	193	_\x8[_\x8L_\x8o_\x8g_\x8o_\x8·_\x8o_\x8f_\x8·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x84_\x8+_\x8d_\x8f_\x8s_\x8g_\x8]
194	\x8\x8\x8\x8·_\x8T\x8T_\x8a\x8a_\x8b\x8b_\x8l\x8l_\x8e\x8e_\x8·_\x8o\x8o_\x8f\x8f_\x8·_\x8C\x8C_\x8o\x8o_\x8n\x8n_\x8t\x8t_\x8e\x8e_\x8n\x8n_\x8t\x8t_\x8s\x8s·\x8\x8\x8\x8	194	\x8\x8\x8\x8·_\x8T\x8T_\x8a\x8a_\x8b\x8b_\x8l\x8l_\x8e\x8e_\x8·_\x8o\x8o_\x8f\x8f_\x8·_\x8C\x8C_\x8o\x8o_\x8n\x8n_\x8t\x8t_\x8e\x8e_\x8n\x8n_\x8t\x8t_\x8s\x8s·\x8\x8\x8\x8
195	····*·_\x8I_\x8n_\x8s_\x8t_\x8a_\x8l_\x8l_\x8i_\x8n_\x8g_\x8·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s	195	····*·_\x8I_\x8n_\x8s_\x8t_\x8a_\x8l_\x8l_\x8i_\x8n_\x8g_\x8·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s


Offset 17, 18 lines modified		Offset 17, 18 lines modified
17	············]	17	············]
18	········},	18	········},
19	········{	19	········{
20	············"cell_type":·"code",	20	············"cell_type":·"code",
21	············"execution_count":·1,	21	············"execution_count":·1,
22	············"metadata":·{	22	············"metadata":·{
23	················"execution":·{	23	················"execution":·{
24	····················"iopub.execute_input":·"2025-12-09T22:24:19.148553Z",	24	····················"iopub.execute_input":·"2024-11-06T18:40:24.782437Z",
25	····················"iopub.status.busy":·"2025-12-09T22:24:19.148293Z",	25	····················"iopub.status.busy":·"2024-11-06T18:40:24.782125Z",
26	····················"iopub.status.idle":·"2025-12-09T22:24:23.~~090176~~Z",	26	····················"iopub.status.idle":·"2024-11-06T18:40:27.234918Z",
27	····················"shell.execute_reply":·"2025-12-09T22:24:23.~~089454~~Z"	27	····················"shell.execute_reply":·"2024-11-06T18:40:27.234217Z"
28	················},	28	················},
29	················"jupyter":·{	29	················"jupyter":·{
30	····················"outputs_hidden":·false	30	····················"outputs_hidden":·false
31	················}	31	················}
32	············},	32	············},
33	············"outputs":·[],	33	············"outputs":·[],
34	············"source":·[	34	············"source":·[
Offset 69, 18 lines modified		Offset 69, 18 lines modified
69	············]	69	············]
70	········},	70	········},
71	········{	71	········{
72	············"cell_type":·"code",	72	············"cell_type":·"code",
73	············"execution_count":·2,	73	············"execution_count":·2,
74	············"metadata":·{	74	············"metadata":·{
75	················"execution":·{	75	················"execution":·{
76	····················"iopub.execute_input":·"2025-12-09T22:24:23.~~093932~~Z",	76	····················"iopub.execute_input":·"2024-11-06T18:40:27.259284Z",
77	····················"iopub.status.busy":·"2025-12-09T22:24:23.~~093643~~Z",	77	····················"iopub.status.busy":·"2024-11-06T18:40:27.258985Z",
78	····················"iopub.status.idle":·"2025-12-09T22:24:23.~~206420~~Z",	78	····················"iopub.status.idle":·"2024-11-06T18:40:27.390936Z",
79	····················"shell.execute_reply":·"2025-12-09T22:24:23.~~2054~~44Z"	79	····················"shell.execute_reply":·"2024-11-06T18:40:27.390240Z"
80	················},	80	················},
81	················"jupyter":·{	81	················"jupyter":·{
82	····················"outputs_hidden":·false	82	····················"outputs_hidden":·false
83	················}	83	················}
84	············},	84	············},
85	············"outputs":·[	85	············"outputs":·[
86	················{	86	················{
Offset 139, 18 lines modified		Offset 139, 18 lines modified
139	············]	139	············]
140	········},	140	········},
141	········{	141	········{
142	············"cell_type":·"code",	142	············"cell_type":·"code",
143	············"execution_count":·3,	143	············"execution_count":·3,
144	············"metadata":·{	144	············"metadata":·{
145	················"execution":·{	145	················"execution":·{
146	····················"iopub.execute_input":·"2025-12-09T22:24:23.~~214427~~Z",	146	····················"iopub.execute_input":·"2024-11-06T18:40:27.397652Z",
147	····················"iopub.status.busy":·"2025-12-09T22:24:23.~~21414~~0Z",	147	····················"iopub.status.busy":·"2024-11-06T18:40:27.397350Z",
148	····················"iopub.status.idle":·"2025-12-09T22:24:23.~~334104~~Z",	148	····················"iopub.status.idle":·"2024-11-06T18:40:27.506919Z",
149	····················"shell.execute_reply":·"2025-12-09T22:24:23.~~333440~~Z"	149	····················"shell.execute_reply":·"2024-11-06T18:40:27.506238Z"
150	················},	150	················},
151	················"jupyter":·{	151	················"jupyter":·{
152	····················"outputs_hidden":·false	152	····················"outputs_hidden":·false
153	················}	153	················}
154	············},	154	············},
155	············"outputs":·[	155	············"outputs":·[
156	················{	156	················{
Offset 215, 18 lines modified		Offset 215, 18 lines modified
215	············]	215	············]
216	········},	216	········},
217	········{	217	········{
218	············"cell_type":·"code",	218	············"cell_type":·"code",
219	············"execution_count":·4,	219	············"execution_count":·4,
220	············"metadata":·{	220	············"metadata":·{
221	················"execution":·{	221	················"execution":·{
222	····················"iopub.execute_input":·"2025-12-09T22:24:23.~~33769~~1Z",	222	····················"iopub.execute_input":·"2024-11-06T18:40:27.513131Z",
223	····················"iopub.status.busy":·"2025-12-09T22:24:23.~~337408~~Z",	223	····················"iopub.status.busy":·"2024-11-06T18:40:27.512836Z",
224	····················"iopub.status.idle":·"2025-12-09T22:24:23.~~354088~~Z",	224	····················"iopub.status.idle":·"2024-11-06T18:40:27.521151Z",
225	····················"shell.execute_reply":·"2025-12-09T22:24:23.~~353~~440Z"	225	····················"shell.execute_reply":·"2024-11-06T18:40:27.520466Z"
226	················},	226	················},
227	················"jupyter":·{	227	················"jupyter":·{
228	····················"outputs_hidden":·false	228	····················"outputs_hidden":·false
229	················}	229	················}
230	············},	230	············},
231	············"outputs":·[	231	············"outputs":·[
232	················{	232	················{
Offset 237, 17 lines modified		Offset 237, 17 lines modified
237	························"-0.020395987154757343\n"	237	························"-0.020395987154757343\n"
238	····················]	238	····················]
239	················},	239	················},
240	················{	240	················{
241	····················"name":·"stderr",	241	····················"name":·"stderr",
242	····················"output_type":·"stream",	242	····················"output_type":·"stream",
243	····················"text":·[	243	····················"text":·[
244	························"/tmp/ipykernel_2897538/1000445862.py:1:·FutureWarning:·Series.__getitem__·treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by·position,·use·`ser.iloc[pos]`\n",	244	························"/tmp/ipykernel_2844558/1000445862.py:1:·FutureWarning:·Series.__getitem__·treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by·position,·use·`ser.iloc[pos]`\n",
245	························"··print(mod1.params[1])\n",	245	························"··print(mod1.params[1])\n",
246	························"/tmp/ipykernel_2897538/1000445862.py:2:·FutureWarning:·Series.__getitem__·treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by·position,·use·`ser.iloc[pos]`\n",	246	························"/tmp/ipykernel_2844558/1000445862.py:2:·FutureWarning:·Series.__getitem__·treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by·position,·use·`ser.iloc[pos]`\n",
247	························"··print(mod2.params[1]·*·2)\n"	247	························"··print(mod2.params[1]·*·2)\n"
248	····················]	248	····················]
249	················}	249	················}
250	············],	250	············],
251	············"source":·[	251	············"source":·[
252	················"print(mod1.params[1])\n",	252	················"print(mod1.params[1])\n",
253	················"print(mod2.params[1]·*·2)"	253	················"print(mod2.params[1]·*·2)"


Offset 18, 18 lines modified		Offset 18, 18 lines modified
18	············]	18	············]
19	········},	19	········},
20	········{	20	········{
21	············"cell_type":·"code",	21	············"cell_type":·"code",
22	············"execution_count":·1,	22	············"execution_count":·1,
23	············"metadata":·{	23	············"metadata":·{
24	················"execution":·{	24	················"execution":·{
25	····················"iopub.execute_input":·"2025-12-09T22:23:57.406384Z",	25	····················"iopub.execute_input":·"2024-11-06T18:40:07.369643Z",
26	····················"iopub.status.busy":·"2025-12-09T22:23:57.~~406116~~Z",	26	····················"iopub.status.busy":·"2024-11-06T18:40:07.369374Z",
27	····················"iopub.status.idle":·"2025-12-09T22:24:00.~~666219~~Z",	27	····················"iopub.status.idle":·"2024-11-06T18:40:11.851025Z",
28	····················"shell.execute_reply":·"2025-12-09T22:24:00.~~665465~~Z"	28	····················"shell.execute_reply":·"2024-11-06T18:40:11.850249Z"
29	················}	29	················}
30	············},	30	············},
31	············"outputs":·[],	31	············"outputs":·[],
32	············"source":·[	32	············"source":·[
33	················"import·pandas·as·pd\n",	33	················"import·pandas·as·pd\n",
34	················"import·numpy·as·np\n",	34	················"import·numpy·as·np\n",
35	················"import·statsmodels.api·as·sm\n",	35	················"import·statsmodels.api·as·sm\n",
Offset 44, 18 lines modified		Offset 44, 18 lines modified
44	············]	44	············]
45	········},	45	········},
46	········{	46	········{
47	············"cell_type":·"code",	47	············"cell_type":·"code",
48	············"execution_count":·2,	48	············"execution_count":·2,
49	············"metadata":·{	49	············"metadata":·{
50	················"execution":·{	50	················"execution":·{
51	····················"iopub.execute_input":·"2025-12-09T22:24:00.~~690563~~Z",	51	····················"iopub.execute_input":·"2024-11-06T18:40:11.855020Z",
52	····················"iopub.status.busy":·"2025-12-09T22:24:00.~~690176~~Z",	52	····················"iopub.status.busy":·"2024-11-06T18:40:11.854610Z",
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54	····················"shell.execute_reply":·"2025-12-09T22:24:00.~~701437~~Z"	54	····················"shell.execute_reply":·"2024-11-06T18:40:11.874256Z"
55	················}	55	················}
56	············},	56	············},
57	············"outputs":·[],	57	············"outputs":·[],
58	············"source":·[	58	············"source":·[
59	················"np.random.seed(3424)"	59	················"np.random.seed(3424)"
60	············]	60	············]
61	········},	61	········},
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67	············]	67	············]
68	········},	68	········},
69	········{	69	········{
70	············"cell_type":·"code",	70	············"cell_type":·"code",
71	············"execution_count":·3,	71	············"execution_count":·3,
72	············"metadata":·{	72	············"metadata":·{
73	················"execution":·{	73	················"execution":·{
74	····················"iopub.execute_input":·"2025-12-09T22:24:00.718~~396~~Z",	74	····················"iopub.execute_input":·"2024-11-06T18:40:11.878855Z",
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77	····················"shell.execute_reply":·"2025-12-09T22:24:00.729440Z"	77	····················"shell.execute_reply":·"2024-11-06T18:40:11.894248Z"
78	················}	78	················}
79	············},	79	············},
80	············"outputs":·[],	80	············"outputs":·[],
81	············"source":·[	81	············"source":·[
82	················"n·=·1000"	82	················"n·=·1000"
83	············]	83	············]
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90	············]	90	············]
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92	········{	92	········{
93	············"cell_type":·"code",	93	············"cell_type":·"code",
94	············"execution_count":·4,	94	············"execution_count":·4,
95	············"metadata":·{	95	············"metadata":·{
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97	····················"iopub.execute_input":·"2025-12-09T22:24:00.~~7464~~22Z",	97	····················"iopub.execute_input":·"2024-11-06T18:40:11.898824Z",
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101	················},	101	················},
102	················"lines_to_next_cell":·1	102	················"lines_to_next_cell":·1
103	············},	103	············},
104	············"outputs":·[],	104	············"outputs":·[],
105	············"source":·[	105	············"source":·[
106	················"exp·=·np.random.normal(size=n)"	106	················"exp·=·np.random.normal(size=n)"
107	············]	107	············]
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114	············]	114	············]
115	········},	115	········},
116	········{	116	········{
117	············"cell_type":·"code",	117	············"cell_type":·"code",
118	············"execution_count":·5,	118	············"execution_count":·5,
119	············"metadata":·{	119	············"metadata":·{
120	················"execution":·{	120	················"execution":·{
121	····················"iopub.execute_input":·"2025-12-09T22:24:00.~~774533~~Z",	121	····················"iopub.execute_input":·"2024-11-06T18:40:11.913187Z",
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124	····················"shell.execute_reply":·"2025-12-09T22:24:00.~~7854~~36Z"	124	····················"shell.execute_reply":·"2024-11-06T18:40:11.927234Z"
125	················},	125	················},
126	················"lines_to_next_cell":·1	126	················"lines_to_next_cell":·1
127	············},	127	············},
128	············"outputs":·[],	128	············"outputs":·[],
129	············"source":·[	129	············"source":·[
130	················"def·gen_mediator():\n",	130	················"def·gen_mediator():\n",
131	················"····mn·=·np.exp(exp)\n",	131	················"····mn·=·np.exp(exp)\n",
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144	············]	144	············]
145	········},	145	········},
146	········{	146	········{
147	············"cell_type":·"code",	147	············"cell_type":·"code",
148	············"execution_count":·6,	148	············"execution_count":·6,
149	············"metadata":·{	149	············"metadata":·{
150	················"execution":·{	150	················"execution":·{
151	····················"iopub.execute_input":·"2025-12-09T22:24:00.~~802423~~Z",	151	····················"iopub.execute_input":·"2024-11-06T18:40:11.931907Z",
152	····················"iopub.status.busy":·"2025-12-09T22:24:00.~~802138~~Z",	152	····················"iopub.status.busy":·"2024-11-06T18:40:11.931617Z",
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154	····················"shell.execute_reply":·"2025-12-09T22:24:00.~~813448~~Z"	154	····················"shell.execute_reply":·"2024-11-06T18:40:11.950235Z"
155	················},	155	················},
156	················"lines_to_next_cell":·1	156	················"lines_to_next_cell":·1
157	············},	157	············},
158	············"outputs":·[],	158	············"outputs":·[],
159	············"source":·[	159	············"source":·[
160	················"def·gen_outcome(otype,·mtime0):\n",	160	················"def·gen_outcome(otype,·mtime0):\n",
161	················"····if·otype·==·\"full\":\n",	161	················"····if·otype·==·\"full\":\n",
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180	············]	180	············]
181	········},	181	········},
182	········{	182	········{
183	············"cell_type":·"code",	183	············"cell_type":·"code",
184	············"execution_count":·7,	184	············"execution_count":·7,
185	············"metadata":·{	185	············"metadata":·{
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187	····················"iopub.execute_input":·"2025-12-09T22:24:00.~~8264~~14Z",	187	····················"iopub.execute_input":·"2024-11-06T18:40:11.954814Z",
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191	················},	191	················},
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24	············]	24	············]
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26	········{	26	········{
27	············"cell_type":·"code",	27	············"cell_type":·"code",
28	············"execution_count":·1,	28	············"execution_count":·1,
29	············"metadata":·{	29	············"metadata":·{
30	················"execution":·{	30	················"execution":·{
31	····················"iopub.execute_input":·"2025-12-09T22:23:57.~~106~~409Z",	31	····················"iopub.execute_input":·"2024-11-06T18:40:04.495430Z",
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34	····················"shell.execute_reply":·"2025-12-09T22:23:58.95~~745~~7Z"	34	····················"shell.execute_reply":·"2024-11-06T18:40:06.458237Z"
35	················}	35	················}
36	············},	36	············},
37	············"outputs":·[],	37	············"outputs":·[],
38	············"source":·[	38	············"source":·[
39	················"%matplotlib·inline"	39	················"%matplotlib·inline"
40	············]	40	············]
41	········},	41	········},
42	········{	42	········{
43	············"cell_type":·"code",	43	············"cell_type":·"code",
44	············"execution_count":·2,	44	············"execution_count":·2,
45	············"metadata":·{	45	············"metadata":·{
46	················"execution":·{	46	················"execution":·{
47	····················"iopub.execute_input":·"2025-12-09T22:23:58.~~9825~~41Z",	47	····················"iopub.execute_input":·"2024-11-06T18:40:06.463348Z",
48	····················"iopub.status.busy":·"2025-12-09T22:23:58.982~~166~~Z",	48	····················"iopub.status.busy":·"2024-11-06T18:40:06.462933Z",
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50	····················"shell.execute_reply":·"2025-12-09T22:24:01.6~~09427~~Z"	50	····················"shell.execute_reply":·"2024-11-06T18:40:09.610253Z"
51	················}	51	················}
52	············},	52	············},
53	············"outputs":·[],	53	············"outputs":·[],
54	············"source":·[	54	············"source":·[
55	················"import·numpy·as·np\n",	55	················"import·numpy·as·np\n",
56	················"import·pandas·as·pd\n",	56	················"import·pandas·as·pd\n",
57	················"from·scipy·import·stats,·optimize\n",	57	················"from·scipy·import·stats,·optimize\n",
Offset 80, 18 lines modified		Offset 80, 18 lines modified
80	············]	80	············]
81	········},	81	········},
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84	············"execution_count":·3,	84	············"execution_count":·3,
85	············"metadata":·{	85	············"metadata":·{
86	················"execution":·{	86	················"execution":·{
87	····················"iopub.execute_input":·"2025-12-09T22:24:01.61~~8614~~Z",	87	····················"iopub.execute_input":·"2024-11-06T18:40:09.617475Z",
88	····················"iopub.status.busy":·"2025-12-09T22:24:01.61~~8185~~Z",	88	····················"iopub.status.busy":·"2024-11-06T18:40:09.617050Z",
89	····················"iopub.status.idle":·"2025-12-09T22:24:01.6~~42250~~Z",	89	····················"iopub.status.idle":·"2024-11-06T18:40:09.655098Z",
90	····················"shell.execute_reply":·"2025-12-09T22:24:01.6~~41552~~Z"	90	····················"shell.execute_reply":·"2024-11-06T18:40:09.654379Z"
91	················}	91	················}
92	············},	92	············},
93	············"outputs":·[	93	············"outputs":·[
94	················{	94	················{
95	····················"data":·{	95	····················"data":·{
96	························"text/plain":·[	96	························"text/plain":·[
97	····························"['Carroll',·'Grant',·'Peck',·'Donat',·'Stewart',·'Young']"	97	····························"['Carroll',·'Grant',·'Peck',·'Donat',·'Stewart',·'Young']"
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118	············]	118	············]
119	········},	119	········},
120	········{	120	········{
121	············"cell_type":·"code",	121	············"cell_type":·"code",
122	············"execution_count":·4,	122	············"execution_count":·4,
123	············"metadata":·{	123	············"metadata":·{
124	················"execution":·{	124	················"execution":·{
125	····················"iopub.execute_input":·"2025-12-09T22:24:01.646132Z",	125	····················"iopub.execute_input":·"2024-11-06T18:40:09.663299Z",
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128	····················"shell.execute_reply":·"2025-12-09T22:24:01.6~~73422~~Z"	128	····················"shell.execute_reply":·"2024-11-06T18:40:09.690216Z"
129	················}	129	················}
130	············},	130	············},
131	············"outputs":·[	131	············"outputs":·[
132	················{	132	················{
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134	························"text/plain":·[	134	························"text/plain":·[
135	····························"['Carroll',·'Grant',·'Peck',·'Donat',·'Stewart',·'Young']"	135	····························"['Carroll',·'Grant',·'Peck',·'Donat',·'Stewart',·'Young']"
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149	············]	149	············]
150	········},	150	········},
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156	····················"iopub.execute_input":·"2025-12-09T22:24:01.677892Z",	156	····················"iopub.execute_input":·"2024-11-06T18:40:09.697811Z",
157	····················"iopub.status.busy":·"2025-12-09T22:24:01.677584Z",	157	····················"iopub.status.busy":·"2024-11-06T18:40:09.697504Z",
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160	················}	160	················}
161	············},	161	············},
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165	························"text/plain":·[	165	························"text/plain":·[
166	····························"array([120,·130,··80,·400,··95,·170])"	166	····························"array([120,·130,··80,·400,··95,·170])"
Offset 183, 18 lines modified		Offset 183, 18 lines modified
183	············]	183	············]
184	········},	184	········},
185	········{	185	········{
186	············"cell_type":·"code",	186	············"cell_type":·"code",
187	············"execution_count":·6,	187	············"execution_count":·6,
188	············"metadata":·{	188	············"metadata":·{
189	················"execution":·{	189	················"execution":·{
190	····················"iopub.execute_input":·"2025-12-09T22:24:01.~~693912~~Z",	190	····················"iopub.execute_input":·"2024-11-06T18:40:09.727378Z",
191	····················"iopub.status.busy":·"2025-12-09T22:24:01.~~693617~~Z",	191	····················"iopub.status.busy":·"2024-11-06T18:40:09.727083Z",
192	····················"iopub.status.idle":·"2025-12-09T22:24:01.7~~06131~~Z",	192	····················"iopub.status.idle":·"2024-11-06T18:40:09.742902Z",
193	····················"shell.execute_reply":·"2025-12-09T22:24:01.7~~05442~~Z"	193	····················"shell.execute_reply":·"2024-11-06T18:40:09.742214Z"
194	················}	194	················}
195	············},	195	············},
196	············"outputs":·[],	196	············"outputs":·[],
197	············"source":·[	197	············"source":·[
198	················"eff,·var_eff·=·effectsize_smd(mean2,·sd2,·nobs2,·mean1,·sd1,·nobs1)"	198	················"eff,·var_eff·=·effectsize_smd(mean2,·sd2,·nobs2,·mean1,·sd1,·nobs1)"
199	············]	199	············]
200	········},	200	········},
Offset 209, 18 lines modified		Offset 209, 18 lines modified
209	············]	209	············]
210	········},	210	········},
211	········{	211	········{
212	············"cell_type":·"code",	212	············"cell_type":·"code",
213	············"execution_count":·7,	213	············"execution_count":·7,
214	············"metadata":·{	214	············"metadata":·{
215	················"execution":·{	215	················"execution":·{
216	····················"iopub.execute_input":·"2025-12-09T22:24:01.7~~0979~~7Z",	216	····················"iopub.execute_input":·"2024-11-06T18:40:09.751457Z",
217	····················"iopub.status.busy":·"2025-12-09T22:24:01.7~~09509~~Z",	217	····················"iopub.status.busy":·"2024-11-06T18:40:09.751154Z",
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219	····················"shell.execute_reply":·"2025-12-09T22:24:01.7~~41415~~Z"	219	····················"shell.execute_reply":·"2024-11-06T18:40:09.798253Z"
220	················}	220	················}
221	············},	221	············},
222	············"outputs":·[	222	············"outputs":·[
223	················{	223	················{
224	····················"name":·"stdout",	224	····················"name":·"stdout",
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Offset 543, 15 lines modified		Offset 543, 15 lines modified
543	</div>	543	</div>
544	</div>	544	</div>
545	<div·class="nboutput·docutils·container">	545	<div·class="nboutput·docutils·container">
546	<div·class="prompt·empty·docutils·container">	546	<div·class="prompt·empty·docutils·container">
547	</div>	547	</div>
548	<div·class="output_area·stderr·docutils·container">	548	<div·class="output_area·stderr·docutils·container">
549	<div·class="highlight"><pre>	549	<div·class="highlight"><pre>
550	/tmp/ipykernel_2895186/427128218.py:3:·UserWarning:·set_ticklabels()·should·only·be·used·with·a·fixed·number·of·ticks,·i.e.·after·set_ticks()·or·using·a·FixedLocator.	550	/tmp/ipykernel_2839140/427128218.py:3:·UserWarning:·set_ticklabels()·should·only·be·used·with·a·fixed·number·of·ticks,·i.e.·after·set_ticks()·or·using·a·FixedLocator.
551	··ax.set_xticklabels(dta.columns.values[::10])	551	··ax.set_xticklabels(dta.columns.values[::10])
552	</pre></div></div>	552	</pre></div></div>
553	</div>	553	</div>
554	<div·class="nboutput·nblast·docutils·container">	554	<div·class="nboutput·nblast·docutils·container">
555	<div·class="prompt·empty·docutils·container">	555	<div·class="prompt·empty·docutils·container">
556	</div>	556	</div>
557	<div·class="output_area·docutils·container">	557	<div·class="output_area·docutils·container">


Offset 126, 15 lines modified		Offset 126, 15 lines modified
126	lines·=·ax.plot(pca_model.factors.iloc[:,·:3],·lw=4,·alpha=0.6)	126	lines·=·ax.plot(pca_model.factors.iloc[:,·:3],·lw=4,·alpha=0.6)
127	ax.set_xticklabels(dta.columns.values[::10])	127	ax.set_xticklabels(dta.columns.values[::10])
128	ax.set_xlim(0,·51)	128	ax.set_xlim(0,·51)
129	ax.set_xlabel("Year",·size=17)	129	ax.set_xlabel("Year",·size=17)
130	fig.subplots_adjust(0.1,·0.1,·0.85,·0.9)	130	fig.subplots_adjust(0.1,·0.1,·0.85,·0.9)
131	legend·=·fig.legend(lines,·["PC·1",·"PC·2",·"PC·3"],·loc="center·right")	131	legend·=·fig.legend(lines,·["PC·1",·"PC·2",·"PC·3"],·loc="center·right")
132	legend.draw_frame(False)	132	legend.draw_frame(False)
133	/tmp/ipykernel_2895186/427128218.py:3:·UserWarning:·set_ticklabels()·should	133	/tmp/ipykernel_2839140/427128218.py:3:·UserWarning:·set_ticklabels()·should
134	only·be·used·with·a·fixed·number·of·ticks,·i.e.·after·set_ticks()·or·using·a	134	only·be·used·with·a·fixed·number·of·ticks,·i.e.·after·set_ticks()·or·using·a
135	FixedLocator.	135	FixedLocator.
136	··ax.set_xticklabels(dta.columns.values[::10])	136	··ax.set_xticklabels(dta.columns.values[::10])
137	[../../../_images/examples_notebooks_generated_pca_fertility_factors_15_1.png]	137	[../../../_images/examples_notebooks_generated_pca_fertility_factors_15_1.png]
138	To·better·understand·what·is·going·on,·we·will·plot·the·fertility·trajectories	138	To·better·understand·what·is·going·on,·we·will·plot·the·fertility·trajectories
139	for·sets·of·countries·with·similar·PC·scores.·The·following·convenience	139	for·sets·of·countries·with·similar·PC·scores.·The·following·convenience
140	function·produces·such·a·plot.	140	function·produces·such·a·plot.


Offset 481, 17 lines modified		Offset 481, 17 lines modified
481	</div>	481	</div>
482	<div·class="output_area·stderr·docutils·container">	482	<div·class="output_area·stderr·docutils·container">
483	<div·class="highlight"><pre>	483	<div·class="highlight"><pre>
484	<>:18:·SyntaxWarning:·invalid·escape·sequence·'\$'	484	<>:18:·SyntaxWarning:·invalid·escape·sequence·'\$'
485	<>:30:·SyntaxWarning:·invalid·escape·sequence·'\$'	485	<>:30:·SyntaxWarning:·invalid·escape·sequence·'\$'
486	<>:18:·SyntaxWarning:·invalid·escape·sequence·'\$'	486	<>:18:·SyntaxWarning:·invalid·escape·sequence·'\$'
487	<>:30:·SyntaxWarning:·invalid·escape·sequence·'\$'	487	<>:30:·SyntaxWarning:·invalid·escape·sequence·'\$'
488	/tmp/ipykernel_28~~90633~~/1205084488.py:18:·SyntaxWarning:·invalid·escape·sequence·'\$'	488	/tmp/ipykernel_2811294/1205084488.py:18:·SyntaxWarning:·invalid·escape·sequence·'\$'
489	··plot_opts["bean_legend_text"]·=·"Income·<·\$30k"	489	··plot_opts["bean_legend_text"]·=·"Income·<·\$30k"
490	/tmp/ipykernel_28~~90633~~/1205084488.py:30:·SyntaxWarning:·invalid·escape·sequence·'\$'	490	/tmp/ipykernel_2811294/1205084488.py:30:·SyntaxWarning:·invalid·escape·sequence·'\$'
491	··plot_opts["bean_legend_text"]·=·"Income·>·\$50k"	491	··plot_opts["bean_legend_text"]·=·"Income·>·\$50k"
492	</pre></div></div>	492	</pre></div></div>
493	</div>	493	</div>
494	<div·class="nboutput·docutils·container">	494	<div·class="nboutput·docutils·container">
495	<div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[15]:	495	<div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[15]:
496	</pre></div>	496	</pre></div>
497	</div>	497	</div>


Offset 238, 18 lines modified		Offset 238, 18 lines modified

238	#·Show·all·plots.	238	#·Show·all·plots.
239	#·plt.show()	239	#·plt.show()
240	<>:18:·SyntaxWarning:·invalid·escape·sequence·'\$'	240	<>:18:·SyntaxWarning:·invalid·escape·sequence·'\$'
241	<>:30:·SyntaxWarning:·invalid·escape·sequence·'\$'	241	<>:30:·SyntaxWarning:·invalid·escape·sequence·'\$'
242	<>:18:·SyntaxWarning:·invalid·escape·sequence·'\$'	242	<>:18:·SyntaxWarning:·invalid·escape·sequence·'\$'
243	<>:30:·SyntaxWarning:·invalid·escape·sequence·'\$'	243	<>:30:·SyntaxWarning:·invalid·escape·sequence·'\$'
244	/tmp/ipykernel_28~~90633~~/1205084488.py:18:·SyntaxWarning:·invalid·escape·sequence	244	/tmp/ipykernel_2811294/1205084488.py:18:·SyntaxWarning:·invalid·escape·sequence
245	'\$'	245	'\$'
246	··plot_opts["bean_legend_text"]·=·"Income·<·\$30k"	246	··plot_opts["bean_legend_text"]·=·"Income·<·\$30k"
247	/tmp/ipykernel_28~~90633~~/1205084488.py:30:·SyntaxWarning:·invalid·escape·sequence	247	/tmp/ipykernel_2811294/1205084488.py:30:·SyntaxWarning:·invalid·escape·sequence
248	'\$'	248	'\$'
249	··plot_opts["bean_legend_text"]·=·"Income·>·\$50k"	249	··plot_opts["bean_legend_text"]·=·"Income·>·\$50k"
250	[15]:	250	[15]:
251	Text(0.5,·1.0,·"US·national·election·'96·-·Age·&·Party·Identification")	251	Text(0.5,·1.0,·"US·national·election·'96·-·Age·&·Party·Identification")
252	[../../../_images/examples_notebooks_generated_plots_boxplots_22_2.png]	252	[../../../_images/examples_notebooks_generated_plots_boxplots_22_2.png]
253	_\x8[_\x8L_\x8o_\x8g_\x8o_\x8·_\x8o_\x8f_\x8·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x84_\x8+_\x8d_\x8f_\x8s_\x8g_\x8]	253	_\x8[_\x8L_\x8o_\x8g_\x8o_\x8·_\x8o_\x8f_\x8·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x84_\x8+_\x8d_\x8f_\x8s_\x8g_\x8]
254	\x8\x8\x8\x8·_\x8T\x8T_\x8a\x8a_\x8b\x8b_\x8l\x8l_\x8e\x8e_\x8·_\x8o\x8o_\x8f\x8f_\x8·_\x8C\x8C_\x8o\x8o_\x8n\x8n_\x8t\x8t_\x8e\x8e_\x8n\x8n_\x8t\x8t_\x8s\x8s·\x8\x8\x8\x8	254	\x8\x8\x8\x8·_\x8T\x8T_\x8a\x8a_\x8b\x8b_\x8l\x8l_\x8e\x8e_\x8·_\x8o\x8o_\x8f\x8f_\x8·_\x8C\x8C_\x8o\x8o_\x8n\x8n_\x8t\x8t_\x8e\x8e_\x8n\x8n_\x8t\x8t_\x8s\x8s·\x8\x8\x8\x8


Offset 174, 17 lines modified		Offset 174, 17 lines modified
174	</div>	174	</div>
175	<div·class="output_area·stderr·docutils·container">	175	<div·class="output_area·stderr·docutils·container">
176	<div·class="highlight"><pre>	176	<div·class="highlight"><pre>
177	<>:5:·SyntaxWarning:·invalid·escape·sequence·'\p'	177	<>:5:·SyntaxWarning:·invalid·escape·sequence·'\p'
178	<>:5:·SyntaxWarning:·invalid·escape·sequence·'\p'	178	<>:5:·SyntaxWarning:·invalid·escape·sequence·'\p'
179	<>:5:·SyntaxWarning:·invalid·escape·sequence·'\p'	179	<>:5:·SyntaxWarning:·invalid·escape·sequence·'\p'
180	<>:5:·SyntaxWarning:·invalid·escape·sequence·'\p'	180	<>:5:·SyntaxWarning:·invalid·escape·sequence·'\p'
181	/tmp/ipykernel_28~~946~~33/3509132601.py:5:·SyntaxWarning:·invalid·escape·sequence·'\p'	181	/tmp/ipykernel_2835534/3509132601.py:5:·SyntaxWarning:·invalid·escape·sequence·'\p'
182	··support,·andrew.weights,·["$-\pia$",·"0",·"$\pia$"],·[-np.pi··a,·0,·np.pi··a]	182	··support,·andrew.weights,·["$-\pia$",·"0",·"$\pia$"],·[-np.pi··a,·0,·np.pi··a]
183	/tmp/ipykernel_28~~946~~33/3509132601.py:5:·SyntaxWarning:·invalid·escape·sequence·'\p'	183	/tmp/ipykernel_2835534/3509132601.py:5:·SyntaxWarning:·invalid·escape·sequence·'\p'
184	··support,·andrew.weights,·["$-\pia$",·"0",·"$\pia$"],·[-np.pi··a,·0,·np.pi··a]	184	··support,·andrew.weights,·["$-\pia$",·"0",·"$\pia$"],·[-np.pi··a,·0,·np.pi··a]
185	</pre></div></div>	185	</pre></div></div>
186	</div>	186	</div>
187	<div·class="nboutput·docutils·container">	187	<div·class="nboutput·docutils·container">
188	<div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[6]:	188	<div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[6]:
189	</pre></div>	189	</pre></div>
190	</div>	190	</div>


Offset 64, 19 lines modified		Offset 64, 19 lines modified
64	····support,·andrew.weights,·["$-\pia$",·"0",·"$\pia$"],·[-np.pi·*·a,·0,	64	····support,·andrew.weights,·["$-\pia$",·"0",·"$\pia$"],·[-np.pi·*·a,·0,
65	np.pi·*·a]	65	np.pi·*·a]
66	)	66	)
67	<>:5:·SyntaxWarning:·invalid·escape·sequence·'\p'	67	<>:5:·SyntaxWarning:·invalid·escape·sequence·'\p'
68	<>:5:·SyntaxWarning:·invalid·escape·sequence·'\p'	68	<>:5:·SyntaxWarning:·invalid·escape·sequence·'\p'
69	<>:5:·SyntaxWarning:·invalid·escape·sequence·'\p'	69	<>:5:·SyntaxWarning:·invalid·escape·sequence·'\p'
70	<>:5:·SyntaxWarning:·invalid·escape·sequence·'\p'	70	<>:5:·SyntaxWarning:·invalid·escape·sequence·'\p'
71	/tmp/ipykernel_28~~946~~33/3509132601.py:5:·SyntaxWarning:·invalid·escape·sequence	71	/tmp/ipykernel_2835534/3509132601.py:5:·SyntaxWarning:·invalid·escape·sequence
72	'\p'	72	'\p'
73	··support,·andrew.weights,·["$-\pia$",·"0",·"$\pia$"],·[-np.pi·*·a,·0,·np.pi	73	··support,·andrew.weights,·["$-\pia$",·"0",·"$\pia$"],·[-np.pi·*·a,·0,·np.pi
74	*·a]	74	*·a]
75	/tmp/ipykernel_28~~946~~33/3509132601.py:5:·SyntaxWarning:·invalid·escape·sequence	75	/tmp/ipykernel_2835534/3509132601.py:5:·SyntaxWarning:·invalid·escape·sequence
76	'\p'	76	'\p'
77	··support,·andrew.weights,·["$-\pia$",·"0",·"$\pia$"],·[-np.pi·*·a,·0,·np.pi	77	··support,·andrew.weights,·["$-\pia$",·"0",·"$\pia$"],·[-np.pi·*·a,·0,·np.pi
78	*·a]	78	*·a]
79	[6]:	79	[6]:
80	<Axes:·>	80	<Axes:·>
81	[../../../_images/examples_notebooks_generated_robust_models_1_9_2.png]	81	[../../../_images/examples_notebooks_generated_robust_models_1_9_2.png]
82	\x8\x8\x8\x8\x8·H\x8Ha\x8am\x8mp\x8pe\x8el\x8l?\x8’s\x8s·1\x817\x87A\x8A_\x8?\x8¶·\x8\x8\x8\x8\x8	82	\x8\x8\x8\x8\x8·H\x8Ha\x8am\x8mp\x8pe\x8el\x8l?\x8’s\x8s·1\x817\x87A\x8A_\x8?\x8¶·\x8\x8\x8\x8\x8


Offset 16, 18 lines modified		Offset 16, 18 lines modified
16	········},	16	········},
17	········{	17	········{
18	············"cell_type":·"code",	18	············"cell_type":·"code",
19	············"execution_count":·1,	19	············"execution_count":·1,
20	············"metadata":·{	20	············"metadata":·{
21	················"collapsed":·false,	21	················"collapsed":·false,
22	················"execution":·{	22	················"execution":·{
23	····················"iopub.execute_input":·"2025-12-09T22:23:29.~~548621~~Z",	23	····················"iopub.execute_input":·"2024-11-06T18:39:31.291230Z",
24	····················"iopub.status.busy":·"2025-12-09T22:23:29.~~5483~~40Z",	24	····················"iopub.status.busy":·"2024-11-06T18:39:31.290942Z",
25	····················"iopub.status.idle":·"2025-12-09T22:23:31.~~086121~~Z",	25	····················"iopub.status.idle":·"2024-11-06T18:39:32.478970Z",
26	····················"shell.execute_reply":·"2025-12-09T22:23:31.085423Z"	26	····················"shell.execute_reply":·"2024-11-06T18:39:32.478242Z"
27	················},	27	················},
28	················"jupyter":·{	28	················"jupyter":·{
29	····················"outputs_hidden":·false	29	····················"outputs_hidden":·false
30	················}	30	················}
31	············},	31	············},
32	············"outputs":·[],	32	············"outputs":·[],
33	············"source":·[	33	············"source":·[
Offset 36, 18 lines modified		Offset 36, 18 lines modified
36	········},	36	········},
37	········{	37	········{
38	············"cell_type":·"code",	38	············"cell_type":·"code",
39	············"execution_count":·2,	39	············"execution_count":·2,
40	············"metadata":·{	40	············"metadata":·{
41	················"collapsed":·false,	41	················"collapsed":·false,
42	················"execution":·{	42	················"execution":·{
43	····················"iopub.execute_input":·"2025-12-09T22:23:31.~~092636~~Z",	43	····················"iopub.execute_input":·"2024-11-06T18:39:32.483118Z",
44	····················"iopub.status.busy":·"2025-12-09T22:23:31.092~~271~~Z",	44	····················"iopub.status.busy":·"2024-11-06T18:39:32.482753Z",
45	····················"iopub.status.idle":·"2025-12-09T22:23:33.~~902165~~Z",	45	····················"iopub.status.idle":·"2024-11-06T18:39:35.293420Z",
46	····················"shell.execute_reply":·"2025-12-09T22:23:33.9~~014~~32Z"	46	····················"shell.execute_reply":·"2024-11-06T18:39:35.292603Z"
47	················},	47	················},
48	················"jupyter":·{	48	················"jupyter":·{
49	····················"outputs_hidden":·false	49	····················"outputs_hidden":·false
50	················}	50	················}
51	············},	51	············},
52	············"outputs":·[],	52	············"outputs":·[],
53	············"source":·[	53	············"source":·[
Offset 61, 18 lines modified		Offset 61, 18 lines modified
61	········},	61	········},
62	········{	62	········{
63	············"cell_type":·"code",	63	············"cell_type":·"code",
64	············"execution_count":·3,	64	············"execution_count":·3,
65	············"metadata":·{	65	············"metadata":·{
66	················"collapsed":·false,	66	················"collapsed":·false,
67	················"execution":·{	67	················"execution":·{
68	····················"iopub.execute_input":·"2025-12-09T22:23:33.910588Z",	68	····················"iopub.execute_input":·"2024-11-06T18:39:35.299459Z",
69	····················"iopub.status.busy":·"2025-12-09T22:23:33.910166Z",	69	····················"iopub.status.busy":·"2024-11-06T18:39:35.299003Z",
70	····················"iopub.status.idle":·"2025-12-09T22:23:33.922~~104~~Z",	70	····················"iopub.status.idle":·"2024-11-06T18:39:35.302811Z",
71	····················"shell.execute_reply":·"2025-12-09T22:23:33.~~921412~~Z"	71	····················"shell.execute_reply":·"2024-11-06T18:39:35.302075Z"
72	················},	72	················},
73	················"jupyter":·{	73	················"jupyter":·{
74	····················"outputs_hidden":·false	74	····················"outputs_hidden":·false
75	················}	75	················}
76	············},	76	············},
77	············"outputs":·[],	77	············"outputs":·[],
78	············"source":·[	78	············"source":·[
Offset 88, 18 lines modified		Offset 88, 18 lines modified
88	········},	88	········},
89	········{	89	········{
90	············"cell_type":·"code",	90	············"cell_type":·"code",
91	············"execution_count":·4,	91	············"execution_count":·4,
92	············"metadata":·{	92	············"metadata":·{
93	················"collapsed":·false,	93	················"collapsed":·false,
94	················"execution":·{	94	················"execution":·{
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96	····················"iopub.status.busy":·"2025-12-09T22:23:33.930~~149~~Z",	96	····················"iopub.status.busy":·"2024-11-06T18:39:35.310952Z",
97	····················"iopub.status.idle":·"2025-12-09T22:23:33.942~~142~~Z",	97	····················"iopub.status.idle":·"2024-11-06T18:39:35.322958Z",
98	····················"shell.execute_reply":·"2025-12-09T22:23:33.~~941429~~Z"	98	····················"shell.execute_reply":·"2024-11-06T18:39:35.322236Z"
99	················},	99	················},
100	················"jupyter":·{	100	················"jupyter":·{
101	····················"outputs_hidden":·false	101	····················"outputs_hidden":·false
102	················}	102	················}
103	············},	103	············},
104	············"outputs":·[	104	············"outputs":·[
105	················{	105	················{
Offset 125, 18 lines modified		Offset 125, 18 lines modified
125	········},	125	········},
126	········{	126	········{
127	············"cell_type":·"code",	127	············"cell_type":·"code",
128	············"execution_count":·5,	128	············"execution_count":·5,
129	············"metadata":·{	129	············"metadata":·{
130	················"collapsed":·false,	130	················"collapsed":·false,
131	················"execution":·{	131	················"execution":·{
132	····················"iopub.execute_input":·"2025-12-09T22:23:33.~~950352~~Z",	132	····················"iopub.execute_input":·"2024-11-06T18:39:35.326771Z",
133	····················"iopub.status.busy":·"2025-12-09T22:23:33.~~95007~~1Z",	133	····················"iopub.status.busy":·"2024-11-06T18:39:35.326481Z",
134	····················"iopub.status.idle":·"2025-12-09T22:23:33.~~9741~~24Z",	134	····················"iopub.status.idle":·"2024-11-06T18:39:35.342928Z",
135	····················"shell.execute_reply":·"2025-12-09T22:23:33.~~973419~~Z"	135	····················"shell.execute_reply":·"2024-11-06T18:39:35.342233Z"
136	················},	136	················},
137	················"jupyter":·{	137	················"jupyter":·{
138	····················"outputs_hidden":·false	138	····················"outputs_hidden":·false
139	················}	139	················}
140	············},	140	············},
141	············"outputs":·[],	141	············"outputs":·[],
142	············"source":·[	142	············"source":·[
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145	········},	145	········},
146	········{	146	········{
147	············"cell_type":·"code",	147	············"cell_type":·"code",
148	············"execution_count":·6,	148	············"execution_count":·6,
149	············"metadata":·{	149	············"metadata":·{
150	················"collapsed":·false,	150	················"collapsed":·false,
151	················"execution":·{	151	················"execution":·{
152	····················"iopub.execute_input":·"2025-12-09T22:23:33.~~98043~~2Z",	152	····················"iopub.execute_input":·"2024-11-06T18:39:35.346882Z",
153	····················"iopub.status.busy":·"2025-12-09T22:23:33.~~980134~~Z",	153	····················"iopub.status.busy":·"2024-11-06T18:39:35.346560Z",
154	····················"iopub.status.idle":·"2025-12-09T22:23:34.~~0020~~97Z",	154	····················"iopub.status.idle":·"2024-11-06T18:39:35.366999Z",
155	····················"shell.execute_reply":·"2025-12-09T22:23:34.~~001430~~Z"	155	····················"shell.execute_reply":·"2024-11-06T18:39:35.366251Z"
156	················},	156	················},
157	················"jupyter":·{	157	················"jupyter":·{
158	····················"outputs_hidden":·false	158	····················"outputs_hidden":·false
159	················}	159	················}
160	············},	160	············},
161	············"outputs":·[],	161	············"outputs":·[],
162	············"source":·[	162	············"source":·[
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166	········},	166	········},
167	········{	167	········{
168	············"cell_type":·"code",	168	············"cell_type":·"code",
169	············"execution_count":·7,	169	············"execution_count":·7,
170	············"metadata":·{	170	············"metadata":·{
171	················"collapsed":·false,	171	················"collapsed":·false,
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174	····················"iopub.status.busy":·"2025-12-09T22:23:34.010~~115~~Z",	174	····················"iopub.status.busy":·"2024-11-06T18:39:35.370464Z",
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176	····················"shell.execute_reply":·"2025-12-09T22:23:34.~~805418~~Z"	176	····················"shell.execute_reply":·"2024-11-06T18:39:36.018244Z"
177	················},	177	················},
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Offset 76, 15 lines modified		Offset 76, 15 lines modified
76	</div>	76	</div>
77	</div>	77	</div>
78	<div·class="nboutput·nblast·docutils·container">	78	<div·class="nboutput·nblast·docutils·container">
79	<div·class="prompt·empty·docutils·container">	79	<div·class="prompt·empty·docutils·container">
80	</div>	80	</div>
81	<div·class="output_area·stderr·docutils·container">	81	<div·class="output_area·stderr·docutils·container">
82	<div·class="highlight"><pre>	82	<div·class="highlight"><pre>
83	/tmp/ipykernel_28~~941~~31/2378637424.py:6:·FutureWarning:·'Q'·is·deprecated·and·will·be·removed·in·a·future·version,·please·use·'QE'·instead.	83	/tmp/ipykernel_2832537/2378637424.py:6:·FutureWarning:·'Q'·is·deprecated·and·will·be·removed·in·a·future·version,·please·use·'QE'·instead.
84	··dta.index·=·pd.date_range(start='1959Q1',·end='2009Q4',·freq='Q')	84	··dta.index·=·pd.date_range(start='1959Q1',·end='2009Q4',·freq='Q')
85	</pre></div></div>	85	</pre></div></div>
86	</div>	86	</div>
87	<section·id="Introduction">	87	<section·id="Introduction">
88	<h2>Introduction<a·class="headerlink"·href="#Introduction"·title="Link·to·this·heading">¶</a></h2>	88	<h2>Introduction<a·class="headerlink"·href="#Introduction"·title="Link·to·this·heading">¶</a></h2>
89	<p>(much·of·this·is·based·on·Harvey·(1989);·see·especially·section·3.4)</p>	89	<p>(much·of·this·is·based·on·Harvey·(1989);·see·especially·section·3.4)</p>
90	<p>State·space·models·can·generically·be·written·as·follows·(here·we·focus·on·time-invariant·state·space·models,·but·similar·results·apply·also·to·time-varying·models):</p>	90	<p>State·space·models·can·generically·be·written·as·follows·(here·we·focus·on·time-invariant·state·space·models,·but·similar·results·apply·also·to·time-varying·models):</p>
Offset 331, 19 lines modified		Offset 331, 19 lines modified
331	</pre></div></div>	331	</pre></div></div>
332	</div>	332	</div>
333	<div·class="nboutput·nblast·docutils·container">	333	<div·class="nboutput·nblast·docutils·container">
334	<div·class="prompt·empty·docutils·container">	334	<div·class="prompt·empty·docutils·container">
335	</div>	335	</div>
336	<div·class="output_area·stderr·docutils·container">	336	<div·class="output_area·stderr·docutils·container">
337	<div·class="highlight"><pre>	337	<div·class="highlight"><pre>
338	/tmp/ipykernel_28~~941~~31/976557282.py:2:·FutureWarning:·Series.__getitem__·treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by·position,·use·`ser.iloc[pos]`	338	/tmp/ipykernel_2832537/976557282.py:2:·FutureWarning:·Series.__getitem__·treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by·position,·use·`ser.iloc[pos]`
339	··print('var.level·····=·%.5f'·%·res.params[0])	339	··print('var.level·····=·%.5f'·%·res.params[0])
340	/tmp/ipykernel_28~~941~~31/976557282.py:3:·FutureWarning:·Series.__getitem__·treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by·position,·use·`ser.iloc[pos]`	340	/tmp/ipykernel_2832537/976557282.py:3:·FutureWarning:·Series.__getitem__·treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by·position,·use·`ser.iloc[pos]`
341	··print('var.irregular·=·%.5f'·%·res.params[1])	341	··print('var.irregular·=·%.5f'·%·res.params[1])
342	/tmp/ipykernel_28~~941~~31/976557282.py:7:·FutureWarning:·Series.__getitem__·treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by·position,·use·`ser.iloc[pos]`	342	/tmp/ipykernel_2832537/976557282.py:7:·FutureWarning:·Series.__getitem__·treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by·position,·use·`ser.iloc[pos]`
343	··print('h··scale·····=·%.5f'·%·(res_conc.params[0]··res_conc.scale))	343	··print('h··scale·····=·%.5f'·%·(res_conc.params[0]··res_conc.scale))
344	</pre></div></div>	344	</pre></div></div>
345	</div>	345	</div>
346	</section>	346	</section>
347	</section>	347	</section>
348	<section·id="Example:-SARIMAX">	348	<section·id="Example:-SARIMAX">
349	<h2>Example:·SARIMAX<a·class="headerlink"·href="#Example:-SARIMAX"·title="Link·to·this·heading">¶</a></h2>	349	<h2>Example:·SARIMAX<a·class="headerlink"·href="#Example:-SARIMAX"·title="Link·to·this·heading">¶</a></h2>


Offset 12, 15 lines modified		Offset 12, 15 lines modified
12	[1]:	12	[1]:
13	import·numpy·as·np	13	import·numpy·as·np
14	import·pandas·as·pd	14	import·pandas·as·pd
15	import·statsmodels.api·as·sm	15	import·statsmodels.api·as·sm

16	dta·=·sm.datasets.macrodata.load_pandas().data	16	dta·=·sm.datasets.macrodata.load_pandas().data
17	dta.index·=·pd.date_range(start='1959Q1',·end='2009Q4',·freq='Q')	17	dta.index·=·pd.date_range(start='1959Q1',·end='2009Q4',·freq='Q')
18	/tmp/ipykernel_28~~941~~31/2378637424.py:6:·FutureWarning:·'Q'·is·deprecated·and	18	/tmp/ipykernel_2832537/2378637424.py:6:·FutureWarning:·'Q'·is·deprecated·and
19	will·be·removed·in·a·future·version,·please·use·'QE'·instead.	19	will·be·removed·in·a·future·version,·please·use·'QE'·instead.
20	··dta.index·=·pd.date_range(start='1959Q1',·end='2009Q4',·freq='Q')	20	··dta.index·=·pd.date_range(start='1959Q1',·end='2009Q4',·freq='Q')
21	\x8\x8\x8\x8\x8·I\x8In\x8nt\x8tr\x8ro\x8od\x8du\x8uc\x8ct\x8ti\x8io\x8on\x8n_\x8?\x8¶·\x8\x8\x8\x8\x8	21	\x8\x8\x8\x8\x8·I\x8In\x8nt\x8tr\x8ro\x8od\x8du\x8uc\x8ct\x8ti\x8io\x8on\x8n_\x8?\x8¶·\x8\x8\x8\x8\x8
22	(much·of·this·is·based·on·Harvey·(1989);·see·especially·section·3.4)	22	(much·of·this·is·based·on·Harvey·(1989);·see·especially·section·3.4)
23	State·space·models·can·generically·be·written·as·follows·(here·we·focus·on	23	State·space·models·can·generically·be·written·as·follows·(here·we·focus·on
24	time-invariant·state·space·models,·but·similar·results·apply·also·to·time-	24	time-invariant·state·space·models,·but·similar·results·apply·also·to·time-
25	varying·models):	25	varying·models):
Offset 245, 25 lines modified		Offset 245, 25 lines modified
245	Original·model	245	Original·model
246	var.level·····=·0.74469	246	var.level·····=·0.74469
247	var.irregular·=·3.37330	247	var.irregular·=·3.37330

248	Concentrated·model	248	Concentrated·model
249	scale·········=·0.74472	249	scale·········=·0.74472
250	h·*·scale·····=·3.37338	250	h·*·scale·····=·3.37338
251	/tmp/ipykernel_28~~941~~31/976557282.py:2:·FutureWarning:·Series.__getitem__	251	/tmp/ipykernel_2832537/976557282.py:2:·FutureWarning:·Series.__getitem__
252	treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys	252	treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys
253	will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To	253	will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To
254	access·a·value·by·position,·use·`ser.iloc[pos]`	254	access·a·value·by·position,·use·`ser.iloc[pos]`
255	··print('var.level·····=·%.5f'·%·res.params[0])	255	··print('var.level·····=·%.5f'·%·res.params[0])
256	/tmp/ipykernel_28~~941~~31/976557282.py:3:·FutureWarning:·Series.__getitem__	256	/tmp/ipykernel_2832537/976557282.py:3:·FutureWarning:·Series.__getitem__
257	treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys	257	treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys
258	will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To	258	will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To
259	access·a·value·by·position,·use·`ser.iloc[pos]`	259	access·a·value·by·position,·use·`ser.iloc[pos]`
260	··print('var.irregular·=·%.5f'·%·res.params[1])	260	··print('var.irregular·=·%.5f'·%·res.params[1])
261	/tmp/ipykernel_28~~941~~31/976557282.py:7:·FutureWarning:·Series.__getitem__	261	/tmp/ipykernel_2832537/976557282.py:7:·FutureWarning:·Series.__getitem__
262	treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys	262	treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys
263	will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To	263	will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To
264	access·a·value·by·position,·use·`ser.iloc[pos]`	264	access·a·value·by·position,·use·`ser.iloc[pos]`
265	··print('h··scale·····=·%.5f'·%·(res_conc.params[0]··res_conc.scale))	265	··print('h··scale·····=·%.5f'·%·(res_conc.params[0]··res_conc.scale))
266	\x8\x8\x8\x8\x8·E\x8Ex\x8xa\x8am\x8mp\x8pl\x8le\x8e:\x8:·S\x8SA\x8AR\x8RI\x8IM\x8MA\x8AX\x8X_\x8?\x8¶·\x8\x8\x8\x8\x8	266	\x8\x8\x8\x8\x8·E\x8Ex\x8xa\x8am\x8mp\x8pl\x8le\x8e:\x8:·S\x8SA\x8AR\x8RI\x8IM\x8MA\x8AX\x8X_\x8?\x8¶·\x8\x8\x8\x8\x8
267	By·default·in·SARIMAX·models,·the·variance·term·is·chosen·by·numerically	267	By·default·in·SARIMAX·models,·the·variance·term·is·chosen·by·numerically
268	maximizing·the·likelihood·function,·but·an·option·has·been·added·to·allow	268	maximizing·the·likelihood·function,·but·an·option·has·been·added·to·allow


Offset 8, 26 lines modified		Offset 8, 26 lines modified
8	············]	8	············]
9	········},	9	········},
10	········{	10	········{
11	············"cell_type":·"code",	11	············"cell_type":·"code",
12	············"execution_count":·1,	12	············"execution_count":·1,
13	············"metadata":·{	13	············"metadata":·{
14	················"execution":·{	14	················"execution":·{
15	····················"iopub.execute_input":·"2025-12-09T22:23:27.4~~94591~~Z",	15	····················"iopub.execute_input":·"2024-11-06T18:39:29.473773Z",
16	····················"iopub.status.busy":·"2025-12-09T22:23:27.4~~942~~92Z",	16	····················"iopub.status.busy":·"2024-11-06T18:39:29.473492Z",
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18	····················"shell.execute_reply":·"2025-12-09T22:23:31.~~081449~~Z"	18	····················"shell.execute_reply":·"2024-11-06T18:39:32.274250Z"
19	················}	19	················}
20	············},	20	············},
21	············"outputs":·[	21	············"outputs":·[
22	················{	22	················{
23	····················"name":·"stderr",	23	····················"name":·"stderr",
24	····················"output_type":·"stream",	24	····················"output_type":·"stream",
25	····················"text":·[	25	····················"text":·[
26	························"/tmp/ipykernel_28~~941~~31/2378637424.py:6:·FutureWarning:·'Q'·is·deprecated·and·will·be·removed·in·a·future·version,·please·use·'QE'·instead.\n",	26	························"/tmp/ipykernel_2832537/2378637424.py:6:·FutureWarning:·'Q'·is·deprecated·and·will·be·removed·in·a·future·version,·please·use·'QE'·instead.\n",
27	························"··dta.index·=·pd.date_range(start='1959Q1',·end='2009Q4',·freq='Q')\n"	27	························"··dta.index·=·pd.date_range(start='1959Q1',·end='2009Q4',·freq='Q')\n"
28	····················]	28	····················]
29	················}	29	················}
30	············],	30	············],
31	············"source":·[	31	············"source":·[
32	················"import·numpy·as·np\n",	32	················"import·numpy·as·np\n",
33	················"import·pandas·as·pd\n",	33	················"import·pandas·as·pd\n",
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89	············]	89	············]
90	········},	90	········},
91	········{	91	········{
92	············"cell_type":·"code",	92	············"cell_type":·"code",
93	············"execution_count":·2,	93	············"execution_count":·2,
94	············"metadata":·{	94	············"metadata":·{
95	················"execution":·{	95	················"execution":·{
96	····················"iopub.execute_input":·"2025-12-09T22:23:31.~~094499~~Z",	96	····················"iopub.execute_input":·"2024-11-06T18:39:32.279135Z",
97	····················"iopub.status.busy":·"2025-12-09T22:23:31.~~0942~~04Z",	97	····················"iopub.status.busy":·"2024-11-06T18:39:32.278807Z",
98	····················"iopub.status.idle":·"2025-12-09T22:23:31.141448Z",	98	····················"iopub.status.idle":·"2024-11-06T18:39:32.291140Z",
99	····················"shell.execute_reply":·"2025-12-09T22:23:31.~~1254~~49Z"	99	····················"shell.execute_reply":·"2024-11-06T18:39:32.290248Z"
100	················}	100	················}
101	············},	101	············},
102	············"outputs":·[],	102	············"outputs":·[],
103	············"source":·[	103	············"source":·[
104	················"class·LocalLevel(sm.tsa.statespace.MLEModel):\n",	104	················"class·LocalLevel(sm.tsa.statespace.MLEModel):\n",
105	················"····_start_params·=·[1.,·1.]\n",	105	················"····_start_params·=·[1.,·1.]\n",
106	················"····_param_names·=·['var.level',·'var.irregular']\n",	106	················"····_param_names·=·['var.level',·'var.irregular']\n",
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135	············]	135	············]
136	········},	136	········},
137	········{	137	········{
138	············"cell_type":·"code",	138	············"cell_type":·"code",
139	············"execution_count":·3,	139	············"execution_count":·3,
140	············"metadata":·{	140	············"metadata":·{
141	················"execution":·{	141	················"execution":·{
142	····················"iopub.execute_input":·"2025-12-09T22:23:31.~~1584~~27Z",	142	····················"iopub.execute_input":·"2024-11-06T18:39:32.295125Z",
143	····················"iopub.status.busy":·"2025-12-09T22:23:31.~~1581~~33Z",	143	····················"iopub.status.busy":·"2024-11-06T18:39:32.294831Z",
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145	····················"shell.execute_reply":·"2025-12-09T22:23:31.~~289402~~Z"	145	····················"shell.execute_reply":·"2024-11-06T18:39:32.398251Z"
146	················}	146	················}
147	············},	147	············},
148	············"outputs":·[	148	············"outputs":·[
149	················{	149	················{
150	····················"name":·"stdout",	150	····················"name":·"stdout",
151	····················"output_type":·"stream",	151	····················"output_type":·"stream",
152	····················"text":·[	152	····················"text":·[
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190	············]	190	············]
191	········},	191	········},
192	········{	192	········{
193	············"cell_type":·"code",	193	············"cell_type":·"code",
194	············"execution_count":·4,	194	············"execution_count":·4,
195	············"metadata":·{	195	············"metadata":·{
196	················"execution":·{	196	················"execution":·{
197	····················"iopub.execute_input":·"2025-12-09T22:23:31.~~318483~~Z",	197	····················"iopub.execute_input":·"2024-11-06T18:39:32.403038Z",
198	····················"iopub.status.busy":·"2025-12-09T22:23:31.~~318189~~Z",	198	····················"iopub.status.busy":·"2024-11-06T18:39:32.402746Z",
199	····················"iopub.status.idle":·"2025-12-09T22:23:31.~~353494~~Z",	199	····················"iopub.status.idle":·"2024-11-06T18:39:32.418959Z",
200	····················"shell.execute_reply":·"2025-12-09T22:23:31.~~337530~~Z"	200	····················"shell.execute_reply":·"2024-11-06T18:39:32.418244Z"
201	················}	201	················}
202	············},	202	············},
203	············"outputs":·[	203	············"outputs":·[
204	················{	204	················{
205	····················"name":·"stdout",	205	····················"name":·"stdout",
206	····················"output_type":·"stream",	206	····················"output_type":·"stream",
207	····················"text":·[	207	····················"text":·[
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245	········},	245	········},
246	········{	246	········{
247	············"cell_type":·"code",	247	············"cell_type":·"code",
248	············"execution_count":·5,	248	············"execution_count":·5,
249	············"metadata":·{	249	············"metadata":·{
250	················"execution":·{	250	················"execution":·{
251	····················"iopub.execute_input":·"2025-12-09T22:23:31.378404Z",	251	····················"iopub.execute_input":·"2024-11-06T18:39:32.422870Z",
252	····················"iopub.status.busy":·"2025-12-09T22:23:31.~~378120~~Z",	252	····················"iopub.status.busy":·"2024-11-06T18:39:32.422573Z",
253	····················"iopub.status.idle":·"2025-12-09T22:23:31.4~~1747~~3Z",	253	····················"iopub.status.idle":·"2024-11-06T18:39:32.438963Z",
254	····················"shell.execute_reply":·"2025-12-09T22:23:31.4~~01456~~Z"	254	····················"shell.execute_reply":·"2024-11-06T18:39:32.438247Z"
255	················}	255	················}
256	············},	256	············},
257	············"outputs":·[],	257	············"outputs":·[],
258	············"source":·[	258	············"source":·[
259	················"class·LocalLevelConcentrated(sm.tsa.statespace.MLEModel):\n",	259	················"class·LocalLevelConcentrated(sm.tsa.statespace.MLEModel):\n",
260	················"····_start_params·=·[1.]\n",	260	················"····_start_params·=·[1.]\n",
261	················"····_param_names·=·['ratio.irregular']\n",	261	················"····_param_names·=·['ratio.irregular']\n",
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289	············]	289	············]
290	········},	290	········},
291	········{	291	········{
292	············"cell_type":·"code",	292	············"cell_type":·"code",
293	············"execution_count":·6,	293	············"execution_count":·6,
294	············"metadata":·{	294	············"metadata":·{
295	················"execution":·{	295	················"execution":·{
296	····················"iopub.execute_input":·"2025-12-09T22:23:31.4~~38447~~Z",	296	····················"iopub.execute_input":·"2024-11-06T18:39:32.442816Z",
297	····················"iopub.status.busy":·"2025-12-09T22:23:31.4~~38161~~Z",	297	····················"iopub.status.busy":·"2024-11-06T18:39:32.442520Z",
298	····················"iopub.status.idle":·"2025-12-09T22:23:31.5~~81469~~Z",	298	····················"iopub.status.idle":·"2024-11-06T18:39:32.530953Z",
299	····················"shell.execute_reply":·"2025-12-09T22:23:31.5~~65451~~Z"	299	····················"shell.execute_reply":·"2024-11-06T18:39:32.530244Z"
300	················}	300	················}
301	············},	301	············},
302	············"outputs":·[	302	············"outputs":·[
303	················{	303	················{
304	····················"name":·"stdout",	304	····················"name":·"stdout",
305	····················"output_type":·"stream",	305	····················"output_type":·"stream",
306	····················"text":·[	306	····················"text":·[
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351	········},	351	········},
352	········{	352	········{
353	············"cell_type":·"code",	353	············"cell_type":·"code",
354	············"execution_count":·7,	354	············"execution_count":·7,
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