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/srv/reproducible-results/rbuild-debian/r-b-build.Sptj02vR/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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control.tar.xz ¶

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control.tar ¶

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data.tar.xz ¶

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data.tar ¶

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343	usr/share/doc/python-statsmodels-doc/html/_images/examples_notebooks_generated_discrete_choice_example_26_1.png	343	usr/share/doc/python-statsmodels-doc/html/_images/examples_notebooks_generated_discrete_choice_example_26_1.png
344	usr/share/doc/python-statsmodels-doc/html/_images/examples_notebooks_generated_discrete_choice_example_55_0.png	344	usr/share/doc/python-statsmodels-doc/html/_images/examples_notebooks_generated_discrete_choice_example_55_0.png
345	usr/share/doc/python-statsmodels-doc/html/_images/examples_notebooks_generated_discrete_choice_example_58_1.png	345	usr/share/doc/python-statsmodels-doc/html/_images/examples_notebooks_generated_discrete_choice_example_58_1.png
346	usr/share/doc/python-statsmodels-doc/html/_images/examples_notebooks_generated_discrete_choice_example_62_1.png	346	usr/share/doc/python-statsmodels-doc/html/_images/examples_notebooks_generated_discrete_choice_example_62_1.png
347	usr/share/doc/python-statsmodels-doc/html/_images/examples_notebooks_generated_discrete_choice_example_64_0.png	347	usr/share/doc/python-statsmodels-doc/html/_images/examples_notebooks_generated_discrete_choice_example_64_0.png
348	usr/share/doc/python-statsmodels-doc/html/_images/examples_notebooks_generated_ets_13_1.png	348	usr/share/doc/python-statsmodels-doc/html/_images/examples_notebooks_generated_ets_13_1.png
349	usr/share/doc/python-statsmodels-doc/html/_images/examples_notebooks_generated_ets_14_3.png	349	usr/share/doc/python-statsmodels-doc/html/_images/examples_notebooks_generated_ets_14_2.png
350	usr/share/doc/python-statsmodels-doc/html/_images/examples_notebooks_generated_ets_21_1.png	350	usr/share/doc/python-statsmodels-doc/html/_images/examples_notebooks_generated_ets_21_1.png
351	usr/share/doc/python-statsmodels-doc/html/_images/examples_notebooks_generated_ets_4_1.png	351	usr/share/doc/python-statsmodels-doc/html/_images/examples_notebooks_generated_ets_4_1.png
352	usr/share/doc/python-statsmodels-doc/html/_images/examples_notebooks_generated_ets_6_2.png	352	usr/share/doc/python-statsmodels-doc/html/_images/examples_notebooks_generated_ets_6_2.png
353	usr/share/doc/python-statsmodels-doc/html/_images/examples_notebooks_generated_ets_8_2.png	353	usr/share/doc/python-statsmodels-doc/html/_images/examples_notebooks_generated_ets_8_2.png
354	usr/share/doc/python-statsmodels-doc/html/_images/examples_notebooks_generated_exponential_smoothing_12_0.png	354	usr/share/doc/python-statsmodels-doc/html/_images/examples_notebooks_generated_exponential_smoothing_12_0.png
355	usr/share/doc/python-statsmodels-doc/html/_images/examples_notebooks_generated_exponential_smoothing_12_1.png	355	usr/share/doc/python-statsmodels-doc/html/_images/examples_notebooks_generated_exponential_smoothing_12_1.png
356	usr/share/doc/python-statsmodels-doc/html/_images/examples_notebooks_generated_exponential_smoothing_14_0.png	356	usr/share/doc/python-statsmodels-doc/html/_images/examples_notebooks_generated_exponential_smoothing_14_0.png


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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_3~~42555~~/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_3604726/2751177292.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>


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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_3~~42555~~/2751177292.py:28:·FutureWarning:·The·'delim_whitespace'	62	/tmp/ipykernel_3604726/2751177292.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·\|


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73	················},	73	················},
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78	············"outputs":·[	78	············"outputs":·[
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80	····················"name":·"stderr",	80	····················"name":·"stderr",
81	····················"output_type":·"stream",	81	····················"output_type":·"stream",
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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"
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43	············"metadata":·{	43	············"metadata":·{
44	················"execution":·{	44	················"execution":·{
45	····················"iopub.execute_input":·"2026-01-03T20:54:45.527145Z",	45	····················"iopub.execute_input":·"2024-12-01T16:18:31.593101Z",
46	····················"iopub.status.busy":·"2026-01-03T20:54:45.526792Z",	46	····················"iopub.status.busy":·"2024-12-01T16:18:31.592707Z",
47	····················"iopub.status.idle":·"2026-01-03T20:54:46.648~~210~~Z",	47	····················"iopub.status.idle":·"2024-12-01T16:18:32.484442Z",
48	····················"shell.execute_reply":·"2026-01-03T20:54:46.~~632247~~Z"	48	····················"shell.execute_reply":·"2024-12-01T16:18:32.478909Z"
49	················}	49	················}
50	············},	50	············},
51	············"outputs":·[],	51	············"outputs":·[],
52	············"source":·[	52	············"source":·[
53	················"import·matplotlib.pyplot·as·plt\n",	53	················"import·matplotlib.pyplot·as·plt\n",
54	················"import·numpy·as·np\n",	54	················"import·numpy·as·np\n",
55	················"import·pandas·as·pd\n",	55	················"import·pandas·as·pd\n",
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59	············]	59	············]
60	········},	60	········},
61	········{	61	········{
62	············"cell_type":·"code",	62	············"cell_type":·"code",
63	············"execution_count":·3,	63	············"execution_count":·3,
64	············"metadata":·{	64	············"metadata":·{
65	················"execution":·{	65	················"execution":·{
66	····················"iopub.execute_input":·"2026-01-03T20:54:46.~~657194~~Z",	66	····················"iopub.execute_input":·"2024-12-01T16:18:32.490437Z",
67	····················"iopub.status.busy":·"2026-01-03T20:54:46.~~656796~~Z",	67	····················"iopub.status.busy":·"2024-12-01T16:18:32.490039Z",
68	····················"iopub.status.idle":·"2026-01-03T20:54:46.~~67684~~3Z",	68	····················"iopub.status.idle":·"2024-12-01T16:18:32.499793Z",
69	····················"shell.execute_reply":·"2026-01-03T20:54:46.~~676147~~Z"	69	····················"shell.execute_reply":·"2024-12-01T16:18:32.495593Z"
70	················}	70	················}
71	············},	71	············},
72	············"outputs":·[	72	············"outputs":·[
73	················{	73	················{
74	····················"name":·"stdout",	74	····················"name":·"stdout",
75	····················"output_type":·"stream",	75	····················"output_type":·"stream",
76	····················"text":·[	76	····················"text":·[
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88	············]	88	············]
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":·"2026-01-03T20:54:46.~~6799~~97Z",	95	····················"iopub.execute_input":·"2024-12-01T16:18:32.506291Z",
96	····················"iopub.status.busy":·"2026-01-03T20:54:46.~~679721~~Z",	96	····················"iopub.status.busy":·"2024-12-01T16:18:32.506010Z",
97	····················"iopub.status.idle":·"2026-01-03T20:54:46.~~688~~861Z",	97	····················"iopub.status.idle":·"2024-12-01T16:18:32.515808Z",
98	····················"shell.execute_reply":·"2026-01-03T20:54:46.~~688~~159Z"	98	····················"shell.execute_reply":·"2024-12-01T16:18:32.515195Z"
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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139	············]	139	············]
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":·"2026-01-03T20:54:46.691927Z",	146	····················"iopub.execute_input":·"2024-12-01T16:18:32.519059Z",
147	····················"iopub.status.busy":·"2026-01-03T20:54:46.~~69165~~3Z",	147	····················"iopub.status.busy":·"2024-12-01T16:18:32.518803Z",
148	····················"iopub.status.idle":·"2026-01-03T20:54:46.~~716870~~Z",	148	····················"iopub.status.idle":·"2024-12-01T16:18:32.534054Z",
149	····················"shell.execute_reply":·"2026-01-03T20:54:46.~~716173~~Z"	149	····················"shell.execute_reply":·"2024-12-01T16:18:32.532048Z"
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":·"2026-01-03T20:54:46.~~720063~~Z",	162	····················"iopub.execute_input":·"2024-12-01T16:18:32.537809Z",
163	····················"iopub.status.busy":·"2026-01-03T20:54:46.~~719769~~Z",	163	····················"iopub.status.busy":·"2024-12-01T16:18:32.537537Z",
164	····················"iopub.status.idle":·"2026-01-03T20:54:46.~~752856~~Z",	164	····················"iopub.status.idle":·"2024-12-01T16:18:32.564730Z",
165	····················"shell.execute_reply":·"2026-01-03T20:54:46.~~7521~~51Z"	165	····················"shell.execute_reply":·"2024-12-01T16:18:32.564050Z"
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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202	············]	202	············]
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":·{
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210	····················"iopub.status.busy":·"2026-01-03T20:54:46.76~~0752~~Z",	210	····················"iopub.status.busy":·"2024-12-01T16:18:32.567265Z",
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212	····················"shell.execute_reply":·"2026-01-03T20:54:46.~~828164~~Z"	212	····················"shell.execute_reply":·"2024-12-01T16:18:32.599905Z"
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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Offset 409, 14 lines modified		Offset 409, 23 lines modified
409	<span·class="nb">print</span><span·class="p">(</span><span·class="n">res_nbin</span><span·class="o">.</span><span·class="n">summary</span><span·class="p">())</span>	409	<span·class="nb">print</span><span·class="p">(</span><span·class="n">res_nbin</span><span·class="o">.</span><span·class="n">summary</span><span·class="p">())</span>
410	</pre></div>	410	</pre></div>
411	</div>	411	</div>
412	</div>	412	</div>
413	<div·class="nboutput·docutils·container">	413	<div·class="nboutput·docutils·container">
414	<div·class="prompt·empty·docutils·container">	414	<div·class="prompt·empty·docutils·container">
415	</div>	415	</div>
		416	<div·class="output_area·stderr·docutils·container">
		417	<div·class="highlight"><pre>
		418	/usr/lib/python3/dist-packages/statsmodels/base/model.py:607:·ConvergenceWarning:·Maximum·Likelihood·optimization·failed·to·converge.·Check·mle_retvals
		419	··warnings.warn("Maximum·Likelihood·optimization·failed·to·"
		420	</pre></div></div>
		421	</div>
		422	<div·class="nboutput·nblast·docutils·container">
		423	<div·class="prompt·empty·docutils·container">
		424	</div>
416	<div·class="output_area·docutils·container">	425	<div·class="output_area·docutils·container">
417	<div·class="highlight"><pre>	426	<div·class="highlight"><pre>
418	·····················NegativeBinomial·Regression·Results	427	·····················NegativeBinomial·Regression·Results
419	==============================================================================	428	==============================================================================
420	Dep.·Variable:··················mdvis···No.·Observations:················20190	429	Dep.·Variable:··················mdvis···No.·Observations:················20190
421	Model:···············NegativeBinomial···Df·Residuals:····················20180	430	Model:···············NegativeBinomial···Df·Residuals:····················20180
422	Method:···························MLE···Df·Model:····························9	431	Method:···························MLE···Df·Model:····························9
Offset 437, 23 lines modified		Offset 446, 14 lines modified
437	hlthf··········0.0173······0.036······0.478······0.632······-0.054·······0.088	446	hlthf··········0.0173······0.036······0.478······0.632······-0.054·······0.088
438	hlthp··········0.1782······0.074······2.399······0.016·······0.033·······0.324	447	hlthp··········0.1782······0.074······2.399······0.016·······0.033·······0.324
439	const··········0.6635······0.025·····26.786······0.000·······0.615·······0.712	448	const··········0.6635······0.025·····26.786······0.000·······0.615·······0.712
440	alpha··········1.2930······0.019·····69.477······0.000·······1.256·······1.329	449	alpha··········1.2930······0.019·····69.477······0.000·······1.256·······1.329
441	==============================================================================	450	==============================================================================
442	</pre></div></div>	451	</pre></div></div>
443	</div>	452	</div>
444	<div·class="nboutput·nblast·docutils·container">
445	<div·class="prompt·empty·docutils·container">
446	</div>
447	<div·class="output_area·stderr·docutils·container">
448	<div·class="highlight"><pre>
449	/usr/lib/python3/dist-packages/statsmodels/base/model.py:607:·ConvergenceWarning:·Maximum·Likelihood·optimization·failed·to·converge.·Check·mle_retvals
450	··warnings.warn("Maximum·Likelihood·optimization·failed·to·"
451	</pre></div></div>
452	</div>
453	</section>	453	</section>
454	<section·id="Alternative-solvers">	454	<section·id="Alternative-solvers">
455	<h2>Alternative·solvers<a·class="headerlink"·href="#Alternative-solvers"·title="Link·to·this·heading">¶</a></h2>	455	<h2>Alternative·solvers<a·class="headerlink"·href="#Alternative-solvers"·title="Link·to·this·heading">¶</a></h2>
456	<p>The·default·method·for·fitting·discrete·data·MLE·models·is·Newton-Raphson.·You·can·use·other·solvers·by·using·the·<code·class="docutils·literal·notranslate"><span·class="pre">method</span></code>·argument:</p>	456	<p>The·default·method·for·fitting·discrete·data·MLE·models·is·Newton-Raphson.·You·can·use·other·solvers·by·using·the·<code·class="docutils·literal·notranslate"><span·class="pre">method</span></code>·argument:</p>
457	<div·class="nbinput·docutils·container">	457	<div·class="nbinput·docutils·container">
458	<div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[15]:	458	<div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[15]:
459	</pre></div>	459	</pre></div>


Offset 195, 14 lines modified		Offset 195, 18 lines modified
195	==============================================================================	195	==============================================================================
196	\x8\x8\x8\x8\x8·N\x8Ne\x8eg\x8ga\x8at\x8ti\x8iv\x8ve\x8e·B\x8Bi\x8in\x8no\x8om\x8mi\x8ia\x8al\x8l_\x8?\x8¶·\x8\x8\x8\x8\x8	196	\x8\x8\x8\x8\x8·N\x8Ne\x8eg\x8ga\x8at\x8ti\x8iv\x8ve\x8e·B\x8Bi\x8in\x8no\x8om\x8mi\x8ia\x8al\x8l_\x8?\x8¶·\x8\x8\x8\x8\x8
197	The·negative·binomial·model·gives·slightly·different·results.	197	The·negative·binomial·model·gives·slightly·different·results.
198	[14]:	198	[14]:
199	mod_nbin·=·sm.NegativeBinomial(rand_data.endog,·rand_exog)	199	mod_nbin·=·sm.NegativeBinomial(rand_data.endog,·rand_exog)
200	res_nbin·=·mod_nbin.fit(disp=False)	200	res_nbin·=·mod_nbin.fit(disp=False)
201	print(res_nbin.summary())	201	print(res_nbin.summary())
		202	/usr/lib/python3/dist-packages/statsmodels/base/model.py:607:
		203	ConvergenceWarning:·Maximum·Likelihood·optimization·failed·to·converge.·Check
		204	mle_retvals
		205	··warnings.warn("Maximum·Likelihood·optimization·failed·to·"
202	·····················NegativeBinomial·Regression·Results	206	·····················NegativeBinomial·Regression·Results
203	==============================================================================	207	==============================================================================
204	Dep.·Variable:··················mdvis···No.·Observations:················20190	208	Dep.·Variable:··················mdvis···No.·Observations:················20190
205	Model:···············NegativeBinomial···Df·Residuals:····················20180	209	Model:···············NegativeBinomial···Df·Residuals:····················20180
206	Method:···························MLE···Df·Model:····························9	210	Method:···························MLE···Df·Model:····························9
207	Date:················Sat,·05·Oct·2024···Pseudo·R-squ.:·················0.01845	211	Date:················Sat,·05·Oct·2024···Pseudo·R-squ.:·················0.01845
208	Time:························10:43:25···Log-Likelihood:················-43384.	212	Time:························10:43:25···Log-Likelihood:················-43384.
Offset 219, 18 lines modified		Offset 223, 14 lines modified
219	disea··········0.0382······0.001·····26.080······0.000·······0.035·······0.041	223	disea··········0.0382······0.001·····26.080······0.000·······0.035·······0.041
220	hlthg·········-0.0441······0.020·····-2.201······0.028······-0.083······-0.005	224	hlthg·········-0.0441······0.020·····-2.201······0.028······-0.083······-0.005
221	hlthf··········0.0173······0.036······0.478······0.632······-0.054·······0.088	225	hlthf··········0.0173······0.036······0.478······0.632······-0.054·······0.088
222	hlthp··········0.1782······0.074······2.399······0.016·······0.033·······0.324	226	hlthp··········0.1782······0.074······2.399······0.016·······0.033·······0.324
223	const··········0.6635······0.025·····26.786······0.000·······0.615·······0.712	227	const··········0.6635······0.025·····26.786······0.000·······0.615·······0.712
224	alpha··········1.2930······0.019·····69.477······0.000·······1.256·······1.329	228	alpha··········1.2930······0.019·····69.477······0.000·······1.256·······1.329
225	==============================================================================	229	==============================================================================
226	/usr/lib/python3/dist-packages/statsmodels/base/model.py:607:
227	ConvergenceWarning:·Maximum·Likelihood·optimization·failed·to·converge.·Check
228	mle_retvals
229	··warnings.warn("Maximum·Likelihood·optimization·failed·to·"
230	\x8\x8\x8\x8\x8·A\x8Al\x8lt\x8te\x8er\x8rn\x8na\x8at\x8ti\x8iv\x8ve\x8e·s\x8so\x8ol\x8lv\x8ve\x8er\x8rs\x8s_\x8?\x8¶·\x8\x8\x8\x8\x8	230	\x8\x8\x8\x8\x8·A\x8Al\x8lt\x8te\x8er\x8rn\x8na\x8at\x8ti\x8iv\x8ve\x8e·s\x8so\x8ol\x8lv\x8ve\x8er\x8rs\x8s_\x8?\x8¶·\x8\x8\x8\x8\x8
231	The·default·method·for·fitting·discrete·data·MLE·models·is·Newton-Raphson.·You	231	The·default·method·for·fitting·discrete·data·MLE·models·is·Newton-Raphson.·You
232	can·use·other·solvers·by·using·the·method·argument:	232	can·use·other·solvers·by·using·the·method·argument:
233	[15]:	233	[15]:
234	mlogit_res·=·mlogit_mod.fit(method="bfgs",·maxiter=250)	234	mlogit_res·=·mlogit_mod.fit(method="bfgs",·maxiter=250)
235	print(mlogit_res.summary())	235	print(mlogit_res.summary())
236	Optimization·terminated·successfully.	236	Optimization·terminated·successfully.


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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":·"2026-01-03T20:54:43.345002Z",	17	····················"iopub.execute_input":·"2024-12-01T16:18:29.755912Z",
18	····················"iopub.status.busy":·"2026-01-03T20:54:43.~~344~~698Z",	18	····················"iopub.status.busy":·"2024-12-01T16:18:29.755643Z",
19	····················"iopub.status.idle":·"2026-01-03T20:54:44.~~204949~~Z",	19	····················"iopub.status.idle":·"2024-12-01T16:18:30.482058Z",
20	····················"shell.execute_reply":·"2026-01-03T20:54:44.~~204~~346Z"	20	····················"shell.execute_reply":·"2024-12-01T16:18:30.481320Z"
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":·"2026-01-03T20:54:44.~~213042~~Z",	68	····················"iopub.execute_input":·"2024-12-01T16:18:30.485893Z",
69	····················"iopub.status.busy":·"2026-01-03T20:54:44.~~212691~~Z",	69	····················"iopub.status.busy":·"2024-12-01T16:18:30.485538Z",
70	····················"iopub.status.idle":·"2026-01-03T20:54:44.~~2248~~18Z",	70	····················"iopub.status.idle":·"2024-12-01T16:18:30.495717Z",
71	····················"shell.execute_reply":·"2026-01-03T20:54:44.~~224148~~Z"	71	····················"shell.execute_reply":·"2024-12-01T16:18:30.491651Z"
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":·"2026-01-03T20:54:44.~~232~~970Z",	95	····················"iopub.execute_input":·"2024-12-01T16:18:30.498933Z",
96	····················"iopub.status.busy":·"2026-01-03T20:54:44.~~232720~~Z",	96	····················"iopub.status.busy":·"2024-12-01T16:18:30.498662Z",
97	····················"iopub.status.idle":·"2026-01-03T20:54:44.376808Z",	97	····················"iopub.status.idle":·"2024-12-01T16:18:30.678586Z",
98	····················"shell.execute_reply":·"2026-01-03T20:54:44.37~~6158~~Z"	98	····················"shell.execute_reply":·"2024-12-01T16:18:30.677864Z"
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":·"2026-01-03T20:54:44.38~~251~~6Z",	121	····················"iopub.execute_input":·"2024-12-01T16:18:30.681906Z",
122	····················"iopub.status.busy":·"2026-01-03T20:54:44.38~~223~~4Z",	122	····················"iopub.status.busy":·"2024-12-01T16:18:30.681624Z",
123	····················"iopub.status.idle":·"2026-01-03T20:54:44.699257Z",	123	····················"iopub.status.idle":·"2024-12-01T16:18:30.992733Z",
124	····················"shell.execute_reply":·"2026-01-03T20:54:44.69~~8635~~Z"	124	····················"shell.execute_reply":·"2024-12-01T16:18:30.992040Z"
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":·"2026-01-03T20:54:44.~~702421~~Z",	152	····················"iopub.execute_input":·"2024-12-01T16:18:30.996557Z",
153	····················"iopub.status.busy":·"2026-01-03T20:54:44.~~70211~~2Z",	153	····················"iopub.status.busy":·"2024-12-01T16:18:30.996272Z",
154	····················"iopub.status.idle":·"2026-01-03T20:54:44.8~~001~~60Z",	154	····················"iopub.status.idle":·"2024-12-01T16:18:31.084736Z",
155	····················"shell.execute_reply":·"2026-01-03T20:54:44.784~~167~~Z"	155	····················"shell.execute_reply":·"2024-12-01T16:18:31.084044Z"
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":·"2026-01-03T20:54:44.807713Z",	183	····················"iopub.execute_input":·"2024-12-01T16:18:31.087803Z",
184	····················"iopub.status.busy":·"2026-01-03T20:54:44.807~~434~~Z",	184	····················"iopub.status.busy":·"2024-12-01T16:18:31.087519Z",
185	····················"iopub.status.idle":·"2026-01-03T20:54:44.~~868219~~Z",	185	····················"iopub.status.idle":·"2024-12-01T16:18:31.112720Z",
186	····················"shell.execute_reply":·"2026-01-03T20:54:44.852154Z"	186	····················"shell.execute_reply":·"2024-12-01T16:18:31.112034Z"
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",


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7612	-rw-r--r--···0·root·········(0)·root·········(0)····56363·2024-10-05·10:43:25.000000·./usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/autoregressions.html	7612	-rw-r--r--···0·root·········(0)·root·········(0)····56363·2024-10-05·10:43:25.000000·./usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/autoregressions.html
7613	-rw-r--r--···0·root·········(0)·root·········(0)····59270·2024-10-05·10:43:25.000000·./usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/autoregressive_distributed_lag.html	7613	-rw-r--r--···0·root·········(0)·root·········(0)····59270·2024-10-05·10:43:25.000000·./usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/autoregressive_distributed_lag.html
7614	-rw-r--r--···0·root·········(0)·root·········(0)·····7234·2024-10-05·10:43:25.000000·./usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/autoregressive_distributed_lag.ipynb.gz	7614	-rw-r--r--···0·root·········(0)·root·········(0)·····7234·2024-10-05·10:43:25.000000·./usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/autoregressive_distributed_lag.ipynb.gz
7615	-rw-r--r--···0·root·········(0)·root·········(0)····12779·2024-10-05·10:43:25.000000·./usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/categorical_interaction_plot.html	7615	-rw-r--r--···0·root·········(0)·root·········(0)····12779·2024-10-05·10:43:25.000000·./usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/categorical_interaction_plot.html
7616	-rw-r--r--···0·root·········(0)·root·········(0)····22135·2024-10-05·10:43:25.000000·./usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/categorical_interaction_plot.ipynb.gz	7616	-rw-r--r--···0·root·········(0)·root·········(0)····22136·2024-10-05·10:43:25.000000·./usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/categorical_interaction_plot.ipynb.gz
7617	-rw-r--r--···0·root·········(0)·root·········(0)····28957·2024-10-05·10:43:25.000000·./usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/chi2_fitting.html	7617	-rw-r--r--···0·root·········(0)·root·········(0)····28958·2024-10-05·10:43:25.000000·./usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/chi2_fitting.html
7618	-rw-r--r--···0·root·········(0)·root·········(0)·····3699·2024-10-05·10:43:25.000000·./usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/chi2_fitting.ipynb.gz	7618	-rw-r--r--···0·root·········(0)·root·········(0)·····3698·2024-10-05·10:43:25.000000·./usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/chi2_fitting.ipynb.gz
7619	-rw-r--r--···0·root·········(0)·root·········(0)····43883·2024-10-05·10:43:25.000000·./usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/contrasts.html	7619	-rw-r--r--···0·root·········(0)·root·········(0)····43883·2024-10-05·10:43:25.000000·./usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/contrasts.html
7620	-rw-r--r--···0·root·········(0)·root·········(0)····24558·2024-10-05·10:43:25.000000·./usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/copula.html	7620	-rw-r--r--···0·root·········(0)·root·········(0)····24558·2024-10-05·10:43:25.000000·./usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/copula.html
7621	-rw-r--r--···0·root·········(0)·root·········(0)···250614·2024-10-05·10:43:25.000000·./usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/copula.ipynb.gz	7621	-rw-r--r--···0·root·········(0)·root·········(0)···250606·2024-10-05·10:43:25.000000·./usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/copula.ipynb.gz
7622	-rw-r--r--···0·root·········(0)·root·········(0)····55918·2024-10-05·10:43:25.000000·./usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/count_hurdle.html	7622	-rw-r--r--···0·root·········(0)·root·········(0)····55918·2024-10-05·10:43:25.000000·./usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/count_hurdle.html
7623	-rw-r--r--···0·root·········(0)·root·········(0)···139507·2024-10-05·10:43:25.000000·./usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/count_hurdle.ipynb.gz	7623	-rw-r--r--···0·root·········(0)·root·········(0)···139511·2024-10-05·10:43:25.000000·./usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/count_hurdle.ipynb.gz
7624	-rw-r--r--···0·root·········(0)·root·········(0)····92750·2024-10-05·10:43:25.000000·./usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/deterministics.html	7624	-rw-r--r--···0·root·········(0)·root·········(0)····92750·2024-10-05·10:43:25.000000·./usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/deterministics.html
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7626	-rw-r--r--···0·root·········(0)·root·········(0)····80991·2024-10-05·10:43:25.000000·./usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/discrete_choice_example.html	7626	-rw-r--r--···0·root·········(0)·root·········(0)····80991·2024-10-05·10:43:25.000000·./usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/discrete_choice_example.html
7627	-rw-r--r--···0·root·········(0)·root·········(0)···237~~413~~·2024-10-05·10:43:25.000000·./usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/discrete_choice_example.ipynb.gz	7627	-rw-r--r--···0·root·········(0)·root·········(0)···237382·2024-10-05·10:43:25.000000·./usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/discrete_choice_example.ipynb.gz
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Offset 176, 14 lines modified		Offset 176, 16 lines modified
176	#·obtained·from·R	176	#·obtained·from·R
177	params·=·[0.99989969,·0.11888177503085334,·0.80000197,·36.46466837,	177	params·=·[0.99989969,·0.11888177503085334,·0.80000197,·36.46466837,
178	34.72584983]	178	34.72584983]
179	yhat·=·model.smooth(params).fittedvalues	179	yhat·=·model.smooth(params).fittedvalues
180	yhat.plot(label="with·R·params",·linestyle=":")	180	yhat.plot(label="with·R·params",·linestyle=":")

181	plt.legend()	181	plt.legend()
		182	[5]:
		183	<matplotlib.legend.Legend·at·0xadde5de1e8ed>
182	RUNNING·THE·L-BFGS-B·CODE	184	RUNNING·THE·L-BFGS-B·CODE

183	·············*	185	·············*

184	Machine·precision·=·2.220D-16	186	Machine·precision·=·2.220D-16
185	·N·=············1·····M·=···········10	187	·N·=············1·····M·=···········10

Offset 206, 16 lines modified		Offset 208, 14 lines modified
206	·············*	208	·············*

207	···N····Tit·····Tnf··Tnint··Skip··Nact·····Projg········F	209	···N····Tit·····Tnf··Tnint··Skip··Nact·····Projg········F
208	····1······1······2······1·····0·····1···0.000D+00···5.317D+00	210	····1······1······2······1·····0·····1···0.000D+00···5.317D+00
209	··F·=···5.3167544390512402	211	··F·=···5.3167544390512402

210	CONVERGENCE:·NORM_OF_PROJECTED_GRADIENT_<=_PGTOL	212	CONVERGENCE:·NORM_OF_PROJECTED_GRADIENT_<=_PGTOL
211	[5]:
212	<matplotlib.legend.Legend·at·0xadde5de1e8ed>
213	[../../../_images/examples_notebooks_generated_ets_8_2.png]	213	[../../../_images/examples_notebooks_generated_ets_8_2.png]
214	The·fitted·parameters·and·some·other·measures·are·shown·using·fit.summary().	214	The·fitted·parameters·and·some·other·measures·are·shown·using·fit.summary().
215	Here·we·can·see·that·the·log-likelihood·of·the·model·using·fitted·initial	215	Here·we·can·see·that·the·log-likelihood·of·the·model·using·fitted·initial
216	states·is·fractionally·lower·than·the·one·using·a·heuristic·for·the·initial	216	states·is·fractionally·lower·than·the·one·using·a·heuristic·for·the·initial
217	states.	217	states.
218	[6]:	218	[6]:
219	print(fit.summary())	219	print(fit.summary())
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")


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_336815/3508103541.py:24:·FutureWarning:·'Y'·is·deprecated·and	133	/tmp/ipykernel_3598929/3508103541.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_336815/3508103541.py:44:·FutureWarning:·'Y'·is·deprecated·and	136	/tmp/ipykernel_3598929/3508103541.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_336815/3508103541.py:80:·FutureWarning:·'Y'·is·deprecated·and	139	/tmp/ipykernel_3598929/3508103541.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_336815/3508103541.py:84:·FutureWarning:·'Y'·is·deprecated·and	142	/tmp/ipykernel_3598929/3508103541.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 230, 27 lines modified		Offset 230, 27 lines modified
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.~~96973~~5</td>	237	······<td>1.048315</td>
238	····</tr>	238	····</tr>
239	····<tr>	239	····<tr>
240	······<th>level1_ix</th>	240	······<th>level1_ix</th>
241	······<td>2.0~~90073~~</td>	241	······<td>2.007618</td>
242	····</tr>	242	····</tr>
243	····<tr>	243	····<tr>
244	······<th>level2_ix</th>	244	······<th>level2_ix</th>
245	······<td>2.~~987231~~</td>	245	······<td>3.008167</td>
246	····</tr>	246	····</tr>
247	····<tr>	247	····<tr>
248	······<th>Residual</th>	248	······<th>Residual</th>
249	······<td>4.~~037248~~</td>	249	······<td>3.998477</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>


Offset 276, 14 lines modified		Offset 276, 23 lines modified
276	<span·class="n">yhat</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">"with·R·params"</span><span·class="p">,</span>·<span·class="n">linestyle</span><span·class="o">=</span><span·class="s2">":"</span><span·class="p">)</span>	276	<span·class="n">yhat</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">"with·R·params"</span><span·class="p">,</span>·<span·class="n">linestyle</span><span·class="o">=</span><span·class="s2">":"</span><span·class="p">)</span>

277	<span·class="n">plt</span><span·class="o">.</span><span·class="n">legend</span><span·class="p">()</span>	277	<span·class="n">plt</span><span·class="o">.</span><span·class="n">legend</span><span·class="p">()</span>
278	</pre></div>	278	</pre></div>
279	</div>	279	</div>
280	</div>	280	</div>
281	<div·class="nboutput·docutils·container">	281	<div·class="nboutput·docutils·container">
		282	<div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[5]:
		283	</pre></div>
		284	</div>
		285	<div·class="output_area·docutils·container">
		286	<div·class="highlight"><pre>
		287	<matplotlib.legend.Legend·at·0xadde5de1e8ed>
		288	</pre></div></div>
		289	</div>
		290	<div·class="nboutput·docutils·container">
282	<div·class="prompt·empty·docutils·container">	291	<div·class="prompt·empty·docutils·container">
283	</div>	292	</div>
284	<div·class="output_area·docutils·container">	293	<div·class="output_area·docutils·container">
285	<div·class="highlight"><pre>	294	<div·class="highlight"><pre>
286	RUNNING·THE·L-BFGS-B·CODE	295	RUNNING·THE·L-BFGS-B·CODE

287	·············*	296	·············*
Offset 312, 23 lines modified		Offset 321, 14 lines modified
312	···N····Tit·····Tnf··Tnint··Skip··Nact·····Projg········F	321	···N····Tit·····Tnf··Tnint··Skip··Nact·····Projg········F
313	····1······1······2······1·····0·····1···0.000D+00···5.317D+00	322	····1······1······2······1·····0·····1···0.000D+00···5.317D+00
314	··F·=···5.3167544390512402	323	··F·=···5.3167544390512402

315	CONVERGENCE:·NORM_OF_PROJECTED_GRADIENT_<=_PGTOL	324	CONVERGENCE:·NORM_OF_PROJECTED_GRADIENT_<=_PGTOL
316	</pre></div></div>	325	</pre></div></div>
317	</div>	326	</div>
318	<div·class="nboutput·docutils·container">
319	<div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[5]:
320	</pre></div>
321	</div>
322	<div·class="output_area·docutils·container">
323	<div·class="highlight"><pre>
324	<matplotlib.legend.Legend·at·0xadde5de1e8ed>
325	</pre></div></div>
326	</div>
327	<div·class="nboutput·nblast·docutils·container">	327	<div·class="nboutput·nblast·docutils·container">
328	<div·class="prompt·empty·docutils·container">	328	<div·class="prompt·empty·docutils·container">
329	</div>	329	</div>
330	<div·class="output_area·docutils·container">	330	<div·class="output_area·docutils·container">
331	<img·alt="../../../_images/examples_notebooks_generated_ets_8_2.png"·src="../../../_images/examples_notebooks_generated_ets_8_2.png"·/>	331	<img·alt="../../../_images/examples_notebooks_generated_ets_8_2.png"·src="../../../_images/examples_notebooks_generated_ets_8_2.png"·/>
332	</div>	332	</div>
333	</div>	333	</div>
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 707, 30 lines modified		Offset 716, 14 lines modified
707	At·iterate···65····f=··2.24461D+00····\|proj·g\|=··5.21290D-03	716	At·iterate···65····f=··2.24461D+00····\|proj·g\|=··5.21290D-03

708	At·iterate···66····f=··2.24459D+00····\|proj·g\|=··2.90856D-03	717	At·iterate···66····f=··2.24459D+00····\|proj·g\|=··2.90856D-03

709	At·iterate···67····f=··2.24457D+00····\|proj·g\|=··2.61871D-03	718	At·iterate···67····f=··2.24457D+00····\|proj·g\|=··2.61871D-03

710	At·iterate···68····f=··2.24455D+00····\|proj·g\|=··2.22808D-03	719	At·iterate···68····f=··2.24455D+00····\|proj·g\|=··2.22808D-03
711	</pre></div></div>
712	</div>
713	<div·class="nboutput·docutils·container">
714	<div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[9]:
715	</pre></div>
716	</div>
717	<div·class="output_area·docutils·container">
718	<div·class="highlight"><pre>
719	<matplotlib.legend.Legend·at·0xadde5de1e8ed>
720	</pre></div></div>
721	</div>
722	<div·class="nboutput·docutils·container">
723	<div·class="prompt·empty·docutils·container">
724	</div>
725	<div·class="output_area·docutils·container">
726	<div·class="highlight"><pre>

727	At·iterate···69····f=··2.24455D+00····\|proj·g\|=··7.23288D-04	720	At·iterate···69····f=··2.24455D+00····\|proj·g\|=··7.23288D-04

728	At·iterate···70····f=··2.24455D+00····\|proj·g\|=··5.35927D-04	721	At·iterate···70····f=··2.24455D+00····\|proj·g\|=··5.35927D-04

729	At·iterate···71····f=··2.24455D+00····\|proj·g\|=··7.26619D-04	722	At·iterate···71····f=··2.24455D+00····\|proj·g\|=··7.26619D-04

Offset 775, 15 lines modified		Offset 768, 15 lines modified
775	CONVERGENCE:·REL_REDUCTION_OF_F_<=_FACTR*EPSMCH	768	CONVERGENCE:·REL_REDUCTION_OF_F_<=_FACTR*EPSMCH
776	</pre></div></div>	769	</pre></div></div>
777	</div>	770	</div>
778	<div·class="nboutput·nblast·docutils·container">	771	<div·class="nboutput·nblast·docutils·container">
779	<div·class="prompt·empty·docutils·container">	772	<div·class="prompt·empty·docutils·container">
780	</div>	773	</div>
781	<div·class="output_area·docutils·container">	774	<div·class="output_area·docutils·container">
782	<img·alt="../../../_images/examples_notebooks_generated_ets_14_3.png"·src="../../../_images/examples_notebooks_generated_ets_14_3.png"·/>	775	<img·alt="../../../_images/examples_notebooks_generated_ets_14_2.png"·src="../../../_images/examples_notebooks_generated_ets_14_2.png"·/>
783	</div>	776	</div>
784	</div>	777	</div>
785	<div·class="nbinput·docutils·container">	778	<div·class="nbinput·docutils·container">
786	<div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[10]:	779	<div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[10]:
787	</pre></div>	780	</pre></div>
788	</div>	781	</div>
789	<div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="nb">print</span><span·class="p">(</span><span·class="n">fit</span><span·class="o">.</span><span·class="n">summary</span><span·class="p">())</span>	782	<div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="nb">print</span><span·class="p">(</span><span·class="n">fit</span><span·class="o">.</span><span·class="n">summary</span><span·class="p">())</span>


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":·"2026-01-03T20:53:48.~~002814~~Z",	28	····················"iopub.execute_input":·"2024-12-01T16:17:44.739109Z",
29	····················"iopub.status.busy":·"2026-01-03T20:53:48.~~002540~~Z",	29	····················"iopub.status.busy":·"2024-12-01T16:17:44.738828Z",
30	····················"iopub.status.idle":·"2026-01-03T20:53:51.~~472949~~Z",	30	····················"iopub.status.idle":·"2024-12-01T16:17:46.364850Z",
31	····················"shell.execute_reply":·"2026-01-03T20:53:51.~~472167~~Z"	31	····················"shell.execute_reply":·"2024-12-01T16:17:46.364092Z"
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":·"2026-01-03T20:53:51.~~4891~~47Z",	50	····················"iopub.execute_input":·"2024-12-01T16:17:46.372243Z",
51	····················"iopub.status.busy":·"2026-01-03T20:53:51.~~488770~~Z",	51	····················"iopub.status.busy":·"2024-12-01T16:17:46.371829Z",
52	····················"iopub.status.idle":·"2026-01-03T20:53:51.~~496826~~Z",	52	····················"iopub.status.idle":·"2024-12-01T16:17:46.380953Z",
53	····················"shell.execute_reply":·"2026-01-03T20:53:51.~~496161~~Z"	53	····················"shell.execute_reply":·"2024-12-01T16:17:46.380204Z"
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	········},
Offset 82, 18 lines modified		Offset 82, 18 lines modified
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":·"2026-01-03T20:53:51.~~504~~978Z",	89	····················"iopub.execute_input":·"2024-12-01T16:17:46.383900Z",
90	····················"iopub.status.busy":·"2026-01-03T20:53:51.504711Z",
91	····················"iopub.status.~~idle~~":·"2026-01-03T20:53:51.~~940854~~Z",	90	····················"iopub.status.busy":·"2024-12-01T16:17:46.383635Z",
		91	····················"iopub.status.idle":·"2024-12-01T16:17:46.616704Z",
92	····················"shell.execute_reply":·"2026-01-03T20:53:51.~~940159~~Z"	92	····················"shell.execute_reply":·"2024-12-01T16:17:46.616044Z"
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)')"
Offset 180, 18 lines modified		Offset 180, 18 lines modified
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":·"2026-01-03T20:53:51.~~9529~~86Z",	187	····················"iopub.execute_input":·"2024-12-01T16:17:46.619587Z",
188	····················"iopub.status.busy":·"2026-01-03T20:53:51.~~95272~~7Z",	188	····················"iopub.status.busy":·"2024-12-01T16:17:46.619317Z",
189	····················"iopub.status.idle":·"2026-01-03T20:53:52.724~~846~~Z",	189	····················"iopub.status.idle":·"2024-12-01T16:17:46.904695Z",
190	····················"shell.execute_reply":·"2026-01-03T20:53:52.724~~166~~Z"	190	····················"shell.execute_reply":·"2024-12-01T16:17:46.904031Z"
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":·[
Offset 277, 22 lines modified		Offset 277, 32 lines modified
277	············]	277	············]
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":·{
284	····················"iopub.execute_input":·"2026-01-03T20:53:52.~~733009~~Z",	284	····················"iopub.execute_input":·"2024-12-01T16:17:46.907477Z",
285	····················"iopub.status.busy":·"2026-01-03T20:53:52.~~732738~~Z",	285	····················"iopub.status.busy":·"2024-12-01T16:17:46.907214Z",
286	····················"iopub.status.idle":·"2026-01-03T20:53:53.~~352~~852Z",	286	····················"iopub.status.idle":·"2024-12-01T16:17:47.216877Z",
287	····················"shell.execute_reply":·"2026-01-03T20:53:53.352169Z"	287	····················"shell.execute_reply":·"2024-12-01T16:17:47.216090Z"
288	················}	288	················}
289	············},	289	············},
290	············"outputs":·[	290	············"outputs":·[
291	················{	291	················{
		292	····················"data":·{
		293	························"text/plain":·[
		294	····························"<matplotlib.legend.Legend·at·0xadde5de1e8ed>"
		295	························]
		296	····················},
		297	····················"execution_count":·5,
		298	····················"metadata":·{},
		299	····················"output_type":·"execute_result"
		300	················},
		301	················{
292	····················"name":·"stdout",	302	····················"name":·"stdout",
293	····················"output_type":·"stream",	303	····················"output_type":·"stream",
294	····················"text":·[	304	····················"text":·[
295	························"RUNNING·THE·L-BFGS-B·CODE\n",	305	························"RUNNING·THE·L-BFGS-B·CODE\n",
296	························"\n",	306	························"\n",
297	························"·············*\n",	307	························"·············*\n",
298	························"\n",	308	························"\n",
Offset 322, 24 lines modified		Offset 332, 14 lines modified
322	························"··F·=···5.3167544390512402·····\n",	332	························"··F·=···5.3167544390512402·····\n",
323	························"\n",	333	························"\n",
324	························"CONVERGENCE:·NORM_OF_PROJECTED_GRADIENT_<=_PGTOL············\n"	334	························"CONVERGENCE:·NORM_OF_PROJECTED_GRADIENT_<=_PGTOL············\n"
325	····················]	335	····················]
326	················},	336	················},
327	················{	337	················{
328	····················"data":·{	338	····················"data":·{
329	························"text/plain":·[
330	····························"<matplotlib.legend.Legend·at·0xadde5de1e8ed>"
331	························]
332	····················},
333	····················"execution_count":·5,
334	····················"metadata":·{},
335	····················"output_type":·"execute_result"
336	················},
337	················{
338	····················"data":·{
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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_336815/3508103541.py:24:·FutureWarning:·'Y'·is·deprecated·and·will·be·removed·in·a·future·version,·please·use·'YE'·instead.	196	/tmp/ipykernel_3598929/3508103541.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_336815/3508103541.py:44:·FutureWarning:·'Y'·is·deprecated·and·will·be·removed·in·a·future·version,·please·use·'YE'·instead.	198	/tmp/ipykernel_3598929/3508103541.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_336815/3508103541.py:80:·FutureWarning:·'Y'·is·deprecated·and·will·be·removed·in·a·future·version,·please·use·'YE'·instead.	200	/tmp/ipykernel_3598929/3508103541.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_336815/3508103541.py:84:·FutureWarning:·'Y'·is·deprecated·and·will·be·removed·in·a·future·version,·please·use·'YE'·instead.	202	/tmp/ipykernel_3598929/3508103541.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>


Offset 79, 18 lines modified		Offset 79, 18 lines modified
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_.._.9_.6_.9_.7_.3_\x85\|	86	\|_\x8g\x8g_\x8r\x8r_\x8o\x8o_\x8u\x8u_\x8p\x8p_\x8s\x8s_\x8_\x8__\x8i\x8i_\x8x\x8x_\x8\|_\x81_.._.0_.4_.8_.3_.1_\x85\|
87	\|_\x8l\x8l_\x8e\x8e_\x8v\x8v_\x8e\x8e_\x8l\x8l_\x81\x81_\x8_\x8__\x8i\x8i_\x8x\x8x_\x8\|_\x82_\x8._\x80_\x89_.0_.0_.7_.3\|	87	\|_\x8l\x8l_\x8e\x8e_\x8v\x8v_\x8e\x8e_\x8l\x8l_\x81\x81_\x8_\x8__\x8i\x8i_\x8x\x8x_\x8\|_\x82_\x8._\x80_\x80_.7_.6_.1_.8\|
88	\|_\x8l\x8l_\x8e\x8e_\x8v\x8v_\x8e\x8e_\x8l\x8l_\x82\x82_\x8_\x8__\x8i\x8i_\x8x\x8x_\x8\|_\x82_.._.9_.8_.7_.2_.3_.1\|	88	\|_\x8l\x8l_\x8e\x8e_\x8v\x8v_\x8e\x8e_\x8l\x8l_\x82\x82_\x8_\x8__\x8i\x8i_\x8x\x8x_\x8\|_\x83_.._.0_.0_.8_.1_.6_.7\|
89	\|_\x8R\x8R_\x8e\x8e_\x8s\x8s_\x8i\x8i_\x8d\x8d_\x8u\x8u_\x8a\x8a_\x8l\x8l_\x8·_\x8\|_\x84_.._.0_.3_.7_.2_.4_.8\|	89	\|_\x8R\x8R_\x8e\x8e_\x8s\x8s_\x8i\x8i_\x8d\x8d_\x8u\x8u_\x8a\x8a_\x8l\x8l_\x8·_\x8\|_\x83_.._.9_.9_.8_.4_.7_.7\|
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 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":·"2026-01-03T20:54:42.~~395310~~Z",	19	····················"iopub.execute_input":·"2024-12-01T16:18:28.708738Z",
20	····················"iopub.status.busy":·"2026-01-03T20:54:42.~~395052~~Z",	20	····················"iopub.status.busy":·"2024-12-01T16:18:28.708406Z",
21	····················"iopub.status.idle":·"2026-01-03T20:54:43.~~616928~~Z",	21	····················"iopub.status.idle":·"2024-12-01T16:18:29.755240Z",
22	····················"shell.execute_reply":·"2026-01-03T20:54:43.~~616231~~Z"	22	····················"shell.execute_reply":·"2024-12-01T16:18:29.754459Z"
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":·"2026-01-03T20:54:43.~~6251~~16Z",	44	····················"iopub.execute_input":·"2024-12-01T16:18:29.758719Z",
45	····················"iopub.status.busy":·"2026-01-03T20:54:43.~~62473~~4Z",	45	····················"iopub.status.busy":·"2024-12-01T16:18:29.758344Z",
46	····················"iopub.status.idle":·"2026-01-03T20:54:43.~~628~~855Z",	46	····················"iopub.status.idle":·"2024-12-01T16:18:29.763870Z",
47	····················"shell.execute_reply":·"2026-01-03T20:54:43.628213Z"	47	····················"shell.execute_reply":·"2024-12-01T16:18:29.761982Z"
48	················}	48	················}
49	············},	49	············},
50	············"outputs":·[],	50	············"outputs":·[],
51	············"source":·[	51	············"source":·[
52	················"p·=·5"	52	················"p·=·5"
53	············]	53	············]
54	········},	54	········},
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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":·"2026-01-03T20:54:43.636~~943~~Z",	67	····················"iopub.execute_input":·"2024-12-01T16:18:29.766735Z",
68	····················"iopub.status.busy":·"2026-01-03T20:54:43.636685Z",	68	····················"iopub.status.busy":·"2024-12-01T16:18:29.766483Z",
69	····················"iopub.status.idle":·"2026-01-03T20:54:43.~~644841~~Z",	69	····················"iopub.status.idle":·"2024-12-01T16:18:29.770576Z",
70	····················"shell.execute_reply":·"2026-01-03T20:54:43.~~644179~~Z"	70	····················"shell.execute_reply":·"2024-12-01T16:18:29.769981Z"
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",
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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":·"2026-01-03T20:54:43.~~652940~~Z",	93	····················"iopub.execute_input":·"2024-12-01T16:18:29.773428Z",
94	····················"iopub.status.busy":·"2026-01-03T20:54:43.~~652681~~Z",	94	····················"iopub.status.busy":·"2024-12-01T16:18:29.773169Z",
95	····················"iopub.status.idle":·"2026-01-03T20:54:43.~~660~~830Z",	95	····················"iopub.status.idle":·"2024-12-01T16:18:29.777890Z",
96	····················"shell.execute_reply":·"2026-01-03T20:54:43.~~660163~~Z"	96	····················"shell.execute_reply":·"2024-12-01T16:18:29.777246Z"
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":·"2026-01-03T20:54:43.~~668940~~Z",	116	····················"iopub.execute_input":·"2024-12-01T16:18:29.780789Z",
117	····················"iopub.status.busy":·"2026-01-03T20:54:43.~~668664~~Z",	117	····················"iopub.status.busy":·"2024-12-01T16:18:29.780533Z",
118	····················"iopub.status.idle":·"2026-01-03T20:54:43.~~676835~~Z",	118	····················"iopub.status.idle":·"2024-12-01T16:18:29.784770Z",
119	····················"shell.execute_reply":·"2026-01-03T20:54:43.676178Z"	119	····················"shell.execute_reply":·"2024-12-01T16:18:29.783795Z"
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":·"2026-01-03T20:54:43.~~696938~~Z",	141	····················"iopub.execute_input":·"2024-12-01T16:18:29.787543Z",
142	····················"iopub.status.busy":·"2026-01-03T20:54:43.~~696668~~Z",	142	····················"iopub.status.busy":·"2024-12-01T16:18:29.787280Z",
143	····················"iopub.status.idle":·"2026-01-03T20:54:43.7~~04811~~Z",	143	····················"iopub.status.idle":·"2024-12-01T16:18:29.791260Z",
144	····················"shell.execute_reply":·"2026-01-03T20:54:43.704150Z"	144	····················"shell.execute_reply":·"2024-12-01T16:18:29.790610Z"
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":·"2026-01-03T20:54:43.7~~20955~~Z",	164	····················"iopub.execute_input":·"2024-12-01T16:18:29.794243Z",
165	····················"iopub.status.busy":·"2026-01-03T20:54:43.7~~206~~89Z",	165	····················"iopub.status.busy":·"2024-12-01T16:18:29.793989Z",
166	····················"iopub.status.idle":·"2026-01-03T20:54:43.~~756831~~Z",	166	····················"iopub.status.idle":·"2024-12-01T16:18:29.813427Z",
167	····················"shell.execute_reply":·"2026-01-03T20:54:43.~~7561~~56Z"	167	····················"shell.execute_reply":·"2024-12-01T16:18:29.812752Z"
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":·"2026-01-03T20:53:48.~~440~~992Z",	21	····················"iopub.execute_input":·"2024-12-01T16:17:44.656973Z",
22	····················"iopub.status.busy":·"2026-01-03T20:53:48.~~440722~~Z",	22	····················"iopub.status.busy":·"2024-12-01T16:17:44.656667Z",
23	····················"iopub.status.idle":·"2026-01-03T20:53:52.~~4408~~86Z",	23	····················"iopub.status.idle":·"2024-12-01T16:17:46.061588Z",
24	····················"shell.execute_reply":·"2026-01-03T20:53:52.440~~175~~Z"	24	····················"shell.execute_reply":·"2024-12-01T16:17:46.060947Z"
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":·"2026-01-03T20:53:52.~~457425~~Z",	49	····················"iopub.execute_input":·"2024-12-01T16:17:46.065054Z",
50	····················"iopub.status.busy":·"2026-01-03T20:53:52.456730Z",	50	····················"iopub.status.busy":·"2024-12-01T16:17:46.064317Z",
51	····················"iopub.status.idle":·"2026-01-03T20:53:52.~~468850~~Z",	51	····················"iopub.status.idle":·"2024-12-01T16:17:46.072788Z",
52	····················"shell.execute_reply":·"2026-01-03T20:53:52.~~468172~~Z"	52	····················"shell.execute_reply":·"2024-12-01T16:17:46.072039Z"
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",
Offset 70, 18 lines modified		Offset 70, 18 lines modified
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":·"2026-01-03T20:53:52.47~~6996~~Z",	77	····················"iopub.execute_input":·"2024-12-01T16:17:46.075809Z",
78	····················"iopub.status.busy":·"2026-01-03T20:53:52.47~~673~~2Z",	78	····················"iopub.status.busy":·"2024-12-01T16:17:46.075552Z",
79	····················"iopub.status.idle":·"2026-01-03T20:53:52.48~~8792~~Z",	79	····················"iopub.status.idle":·"2024-12-01T16:17:46.083587Z",
80	····················"shell.execute_reply":·"2026-01-03T20:53:52.48~~8153~~Z"	80	····················"shell.execute_reply":·"2024-12-01T16:17:46.082905Z"
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":·"2026-01-03T20:53:52.496930Z",	113	····················"iopub.execute_input":·"2024-12-01T16:17:46.086335Z",
114	····················"iopub.status.busy":·"2026-01-03T20:53:52.496667Z",
115	····················"iopub.status.~~idle~~":·"2026-01-03T20:53:52.508~~928~~Z",	114	····················"iopub.status.busy":·"2024-12-01T16:17:46.086072Z",
		115	····················"iopub.status.idle":·"2024-12-01T16:17:46.096326Z",
116	····················"shell.execute_reply":·"2026-01-03T20:53:52.~~508155~~Z"	116	····················"shell.execute_reply":·"2024-12-01T16:17:46.094313Z"
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"
Offset 131, 18 lines modified		Offset 131, 18 lines modified
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":·"2026-01-03T20:53:52.~~516971~~Z",	138	····················"iopub.execute_input":·"2024-12-01T16:17:46.099147Z",
139	····················"iopub.status.busy":·"2026-01-03T20:53:52.~~516699~~Z",	139	····················"iopub.status.busy":·"2024-12-01T16:17:46.098870Z",
140	····················"iopub.status.idle":·"2026-01-03T20:53:52.528~~836~~Z",	140	····················"iopub.status.idle":·"2024-12-01T16:17:46.108758Z",
141	····················"shell.execute_reply":·"2026-01-03T20:53:52.528~~167~~Z"	141	····················"shell.execute_reply":·"2024-12-01T16:17:46.108070Z"
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":·"2026-01-03T20:53:52.536945Z",	161	····················"iopub.execute_input":·"2024-12-01T16:17:46.113234Z",
162	····················"iopub.status.busy":·"2026-01-03T20:53:52.~~536680~~Z",	162	····················"iopub.status.busy":·"2024-12-01T16:17:46.112953Z",
163	····················"iopub.status.idle":·"2026-01-03T20:53:52.~~54883~~8Z",	163	····················"iopub.status.idle":·"2024-12-01T16:17:46.122198Z",
164	····················"shell.execute_reply":·"2026-01-03T20:53:52.~~5481~~57Z"	164	····················"shell.execute_reply":·"2024-12-01T16:17:46.121558Z"
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	············]
Offset 178, 18 lines modified		Offset 178, 18 lines modified
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":·"2026-01-03T20:53:52.~~556971~~Z",	185	····················"iopub.execute_input":·"2024-12-01T16:17:46.125186Z",
186	····················"iopub.status.busy":·"2026-01-03T20:53:52.~~556698~~Z",	186	····················"iopub.status.busy":·"2024-12-01T16:17:46.124901Z",
187	····················"iopub.status.idle":·"2026-01-03T20:53:52.~~568840~~Z",	187	····················"iopub.status.idle":·"2024-12-01T16:17:46.132181Z",
188	····················"shell.execute_reply":·"2026-01-03T20:53:52.~~568155~~Z"	188	····················"shell.execute_reply":·"2024-12-01T16:17:46.131472Z"
189	················}	189	················}
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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":·"2026-01-03T20:53:47.890~~122~~Z",	34	····················"iopub.execute_input":·"2024-12-01T16:17:44.580905Z",
35	····················"iopub.status.busy":·"2026-01-03T20:53:47.88~~9868~~Z",	35	····················"iopub.status.busy":·"2024-12-01T16:17:44.580614Z",
36	····················"iopub.status.idle":·"2026-01-03T20:53:50.~~544231~~Z",	36	····················"iopub.status.idle":·"2024-12-01T16:17:45.736062Z",
37	····················"shell.execute_reply":·"2026-01-03T20:53:50.52~~8166~~Z"	37	····················"shell.execute_reply":·"2024-12-01T16:17:45.720040Z"
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":·[
Offset 56, 18 lines modified		Offset 56, 18 lines modified
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":·"2026-01-03T20:53:50.~~561122~~Z",	63	····················"iopub.execute_input":·"2024-12-01T16:17:45.757038Z",
64	····················"iopub.status.busy":·"2026-01-03T20:53:50.560~~742~~Z",	64	····················"iopub.status.busy":·"2024-12-01T16:17:45.756616Z",
65	····················"iopub.status.idle":·"2026-01-03T20:53:50.62~~422~~3Z",	65	····················"iopub.status.idle":·"2024-12-01T16:17:45.820063Z",
66	····················"shell.execute_reply":·"2026-01-03T20:53:50.60~~8161~~Z"	66	····················"shell.execute_reply":·"2024-12-01T16:17:45.804035Z"
67	················},	67	················},
68	················"jupyter":·{	68	················"jupyter":·{
69	····················"outputs_hidden":·false	69	····················"outputs_hidden":·false
70	················}	70	················}
71	············},	71	············},
72	············"outputs":·[	72	············"outputs":·[
73	················{	73	················{
Offset 113, 18 lines modified		Offset 113, 18 lines modified
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":·"2026-01-03T20:53:50.708983Z",	120	····················"iopub.execute_input":·"2024-12-01T16:17:45.872879Z",
121	····················"iopub.status.busy":·"2026-01-03T20:53:50.708713Z",	121	····················"iopub.status.busy":·"2024-12-01T16:17:45.872576Z",
122	····················"iopub.status.idle":·"2026-01-03T20:53:50.~~740186~~Z",	122	····················"iopub.status.idle":·"2024-12-01T16:17:45.916052Z",
123	····················"shell.execute_reply":·"2026-01-03T20:53:50.~~724175~~Z"	123	····················"shell.execute_reply":·"2024-12-01T16:17:45.896033Z"
124	················},	124	················},
125	················"jupyter":·{	125	················"jupyter":·{
126	····················"outputs_hidden":·false	126	····················"outputs_hidden":·false
127	················}	127	················}
128	············},	128	············},
129	············"outputs":·[],	129	············"outputs":·[],
130	············"source":·[	130	············"source":·[
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139	············]	139	············]
140	········},	140	········},
141	········{	141	········{
142	············"cell_type":·"code",	142	············"cell_type":·"code",
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23	················"%matplotlib·inline"	23	················"%matplotlib·inline"
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38	············"source":·[	38	············"source":·[
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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70	················}	70	················}
71	············},	71	············},
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73	················{	73	················{
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128	············]	128	············]
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139	················}	139	················}
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142	············"source":·[	142	············"source":·[
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)"
145	············]	145	············]
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153	········},	153	········},
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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_3~~419~~21/1000445862.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_3603120/1000445862.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_3~~419~~21/1000445862.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_3603120/1000445862.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_3~~419~~21/1000445862.py:1:·FutureWarning:·Series.__getitem__	183	/tmp/ipykernel_3603120/1000445862.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_3~~419~~21/1000445862.py:2:·FutureWarning:·Series.__getitem__	188	/tmp/ipykernel_3603120/1000445862.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":·"2026-01-03T20:54:41.308~~954~~Z",	24	····················"iopub.execute_input":·"2024-12-01T16:18:27.498023Z",
25	····················"iopub.status.busy":·"2026-01-03T20:54:41.~~308699~~Z",	25	····················"iopub.status.busy":·"2024-12-01T16:18:27.497544Z",
26	····················"iopub.status.idle":·"2026-01-03T20:54:42.~~488984~~Z",	26	····················"iopub.status.idle":·"2024-12-01T16:18:28.531620Z",
27	····················"shell.execute_reply":·"2026-01-03T20:54:42.~~488227~~Z"	27	····················"shell.execute_reply":·"2024-12-01T16:18:28.530960Z"
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":·"2026-01-03T20:54:42.5~~01067~~Z",	76	····················"iopub.execute_input":·"2024-12-01T16:18:28.534451Z",
77	····················"iopub.status.busy":·"2026-01-03T20:54:42.5~~00781~~Z",	77	····················"iopub.status.busy":·"2024-12-01T16:18:28.534179Z",
78	····················"iopub.status.idle":·"2026-01-03T20:54:42.544~~791~~Z",	78	····················"iopub.status.idle":·"2024-12-01T16:18:28.574270Z",
79	····················"shell.execute_reply":·"2026-01-03T20:54:42.5~~441~~38Z"	79	····················"shell.execute_reply":·"2024-12-01T16:18:28.573538Z"
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":·"2026-01-03T20:54:42.5~~52945~~Z",	146	····················"iopub.execute_input":·"2024-12-01T16:18:28.577237Z",
147	····················"iopub.status.busy":·"2026-01-03T20:54:42.5~~52670~~Z",	147	····················"iopub.status.busy":·"2024-12-01T16:18:28.576489Z",
148	····················"iopub.status.idle":·"2026-01-03T20:54:42.6~~00965~~Z",	148	····················"iopub.status.idle":·"2024-12-01T16:18:28.613830Z",
149	····················"shell.execute_reply":·"2026-01-03T20:54:42.6~~00161~~Z"	149	····················"shell.execute_reply":·"2024-12-01T16:18:28.613057Z"
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":·"2026-01-03T20:54:42.606454Z",	222	····················"iopub.execute_input":·"2024-12-01T16:18:28.616745Z",
223	····················"iopub.status.busy":·"2026-01-03T20:54:42.606120Z",	223	····················"iopub.status.busy":·"2024-12-01T16:18:28.616326Z",
224	····················"iopub.status.idle":·"2026-01-03T20:54:42.6~~44165~~Z",	224	····················"iopub.status.idle":·"2024-12-01T16:18:28.622773Z",
225	····················"shell.execute_reply":·"2026-01-03T20:54:42.62~~8139~~Z"	225	····················"shell.execute_reply":·"2024-12-01T16:18:28.621645Z"
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_3~~419~~21/1000445862.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_3603120/1000445862.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_3~~419~~21/1000445862.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_3603120/1000445862.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":·"2026-01-03T20:54:32.~~240902~~Z",	25	····················"iopub.execute_input":·"2024-12-01T16:18:20.517873Z",
26	····················"iopub.status.busy":·"2026-01-03T20:54:32.~~240~~652Z",	26	····················"iopub.status.busy":·"2024-12-01T16:18:20.517605Z",
27	····················"iopub.status.idle":·"2026-01-03T20:54:33.~~7284~~45Z",	27	····················"iopub.status.idle":·"2024-12-01T16:18:21.652742Z",
28	····················"shell.execute_reply":·"2026-01-03T20:54:33.720199Z"	28	····················"shell.execute_reply":·"2024-12-01T16:18:21.652049Z"
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":·"2026-01-03T20:54:33.~~737215~~Z",	51	····················"iopub.execute_input":·"2024-12-01T16:18:21.669040Z",
52	····················"iopub.status.busy":·"2026-01-03T20:54:33.736856Z",	52	····················"iopub.status.busy":·"2024-12-01T16:18:21.668623Z",
53	····················"iopub.status.idle":·"2026-01-03T20:54:33.744~~800~~Z",	53	····················"iopub.status.idle":·"2024-12-01T16:18:21.674035Z",
54	····················"shell.execute_reply":·"2026-01-03T20:54:33.~~74415~~8Z"	54	····················"shell.execute_reply":·"2024-12-01T16:18:21.673378Z"
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	········},
Offset 67, 18 lines modified		Offset 67, 18 lines modified
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":·"2026-01-03T20:54:33.747617Z",	74	····················"iopub.execute_input":·"2024-12-01T16:18:21.676790Z",
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77	····················"shell.execute_reply":·"2026-01-03T20:54:33.~~753735~~Z"	77	····················"shell.execute_reply":·"2024-12-01T16:18:21.680147Z"
78	················}	78	················}
79	············},	79	············},
80	············"outputs":·[],	80	············"outputs":·[],
81	············"source":·[	81	············"source":·[
82	················"n·=·1000"	82	················"n·=·1000"
83	············]	83	············]
84	········},	84	········},
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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":·{
96	················"execution":·{	96	················"execution":·{
97	····················"iopub.execute_input":·"2026-01-03T20:54:33.~~757199~~Z",	97	····················"iopub.execute_input":·"2024-12-01T16:18:21.683704Z",
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100	····················"shell.execute_reply":·"2026-01-03T20:54:33.~~763860~~Z"	100	····················"shell.execute_reply":·"2024-12-01T16:18:21.689134Z"
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":·"2026-01-03T20:54:33.778286Z",
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124	····················"shell.execute_reply":·"2026-01-03T20:54:33.7~~8817~~6Z"	124	····················"shell.execute_reply":·"2024-12-01T16:18:21.704026Z"
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":·"2026-01-03T20:54:33.7~~91684~~Z",	151	····················"iopub.execute_input":·"2024-12-01T16:18:21.707771Z",
152	····················"iopub.status.busy":·"2026-01-03T20:54:33.7~~91431~~Z",	152	····················"iopub.status.busy":·"2024-12-01T16:18:21.707504Z",
153	····················"iopub.status.idle":·"2026-01-03T20:54:33.800825Z",
154	····················"~~shell~~.ex~~ecu~~t~~e_rep~~ly":·"2026-01-03T20:54:33.~~800156~~Z"	153	····················"iopub.status.idle":·"2024-12-01T16:18:21.714319Z",
		154	····················"shell.execute_reply":·"2024-12-01T16:18:21.713079Z"
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":·{
186	················"execution":·{	186	················"execution":·{
187	····················"iopub.execute_input":·"2026-01-03T20:54:33.803713Z",	187	····················"iopub.execute_input":·"2024-12-01T16:18:21.717376Z",
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Offset 24, 34 lines modified		Offset 24, 34 lines modified
24	············]	24	············]
25	········},	25	········},
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":·"2026-01-03T20:54:31.~~8866~~69Z",	31	····················"iopub.execute_input":·"2024-12-01T16:18:20.407067Z",
32	····················"iopub.status.busy":·"2026-01-03T20:54:31.886~~374~~Z",	32	····················"iopub.status.busy":·"2024-12-01T16:18:20.406196Z",
33	····················"iopub.status.idle":·"2026-01-03T20:54:32.820~~957~~Z",	33	····················"iopub.status.idle":·"2024-12-01T16:18:21.260039Z",
34	····················"shell.execute_reply":·"2026-01-03T20:54:32.~~820164~~Z"	34	····················"shell.execute_reply":·"2024-12-01T16:18:21.259388Z"
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":·"2026-01-03T20:54:32.~~829~~051Z",	47	····················"iopub.execute_input":·"2024-12-01T16:18:21.273084Z",
48	····················"iopub.status.busy":·"2026-01-03T20:54:32.~~828~~693Z",	48	····················"iopub.status.busy":·"2024-12-01T16:18:21.272684Z",
49	····················"iopub.status.idle":·"2026-01-03T20:54:33.~~600190~~Z",	49	····················"iopub.status.idle":·"2024-12-01T16:18:22.084714Z",
50	····················"shell.execute_reply":·"2026-01-03T20:54:33.58~~820~~7Z"	50	····················"shell.execute_reply":·"2024-12-01T16:18:22.084017Z"
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	········},
82	········{	82	········{
83	············"cell_type":·"code",	83	············"cell_type":·"code",
84	············"execution_count":·3,	84	············"execution_count":·3,
85	············"metadata":·{	85	············"metadata":·{
86	················"execution":·{	86	················"execution":·{
87	····················"iopub.execute_input":·"2026-01-03T20:54:33.613153Z",	87	····················"iopub.execute_input":·"2024-12-01T16:18:22.101034Z",
88	····················"iopub.status.busy":·"2026-01-03T20:54:33.~~612757~~Z",	88	····················"iopub.status.busy":·"2024-12-01T16:18:22.100612Z",
89	····················"iopub.status.idle":·"2026-01-03T20:54:33.62~~7571~~Z",	89	····················"iopub.status.idle":·"2024-12-01T16:18:22.128389Z",
90	····················"shell.execute_reply":·"2026-01-03T20:54:33.62~~6940~~Z"	90	····················"shell.execute_reply":·"2024-12-01T16:18:22.123827Z"
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']"
Offset 118, 18 lines modified		Offset 118, 18 lines modified
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":·"2026-01-03T20:54:33.63~~6909~~Z",	125	····················"iopub.execute_input":·"2024-12-01T16:18:22.131143Z",
126	····················"iopub.status.busy":·"2026-01-03T20:54:33.63~~6646~~Z",	126	····················"iopub.status.busy":·"2024-12-01T16:18:22.130881Z",
127	····················"iopub.status.idle":·"2026-01-03T20:54:33.688~~143~~Z",	127	····················"iopub.status.idle":·"2024-12-01T16:18:22.138800Z",
128	····················"shell.execute_reply":·"2026-01-03T20:54:33.~~672~~126Z"	128	····················"shell.execute_reply":·"2024-12-01T16:18:22.138165Z"
129	················}	129	················}
130	············},	130	············},
131	············"outputs":·[	131	············"outputs":·[
132	················{	132	················{
133	····················"data":·{	133	····················"data":·{
134	························"text/plain":·[	134	························"text/plain":·[
135	····························"['Carroll',·'Grant',·'Peck',·'Donat',·'Stewart',·'Young']"	135	····························"['Carroll',·'Grant',·'Peck',·'Donat',·'Stewart',·'Young']"
Offset 149, 18 lines modified		Offset 149, 18 lines modified
149	············]	149	············]
150	········},	150	········},
151	········{	151	········{
152	············"cell_type":·"code",	152	············"cell_type":·"code",
153	············"execution_count":·5,	153	············"execution_count":·5,
154	············"metadata":·{	154	············"metadata":·{
155	················"execution":·{	155	················"execution":·{
156	····················"iopub.execute_input":·"2026-01-03T20:54:33.~~69692~~9Z",	156	····················"iopub.execute_input":·"2024-12-01T16:18:22.141519Z",
157	····················"iopub.status.busy":·"2026-01-03T20:54:33.~~6966~~67Z",	157	····················"iopub.status.busy":·"2024-12-01T16:18:22.141262Z",
158	····················"iopub.status.idle":·"2026-01-03T20:54:33.712739Z",	158	····················"iopub.status.idle":·"2024-12-01T16:18:22.147476Z",
159	····················"shell.execute_reply":·"2026-01-03T20:54:33.71~~214~~0Z"	159	····················"shell.execute_reply":·"2024-12-01T16:18:22.146908Z"
160	················}	160	················}
161	············},	161	············},
162	············"outputs":·[	162	············"outputs":·[
163	················{	163	················{
164	····················"data":·{	164	····················"data":·{
165	························"text/plain":·[	165	························"text/plain":·[
166	····························"array([120,·130,··80,·400,··95,·170])"	166	····························"array([120,·130,··80,·400,··95,·170])"
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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":·"2026-01-03T20:54:33.720~~908~~Z",	190	····················"iopub.execute_input":·"2024-12-01T16:18:22.150342Z",
191	····················"iopub.status.busy":·"2026-01-03T20:54:33.720~~656~~Z",	191	····················"iopub.status.busy":·"2024-12-01T16:18:22.150080Z",
192	····················"iopub.status.idle":·"2026-01-03T20:54:33.~~728771~~Z",	192	····················"iopub.status.idle":·"2024-12-01T16:18:22.159109Z",
193	····················"shell.execute_reply":·"2026-01-03T20:54:33.728~~140~~Z"	193	····················"shell.execute_reply":·"2024-12-01T16:18:22.158385Z"
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	········},
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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":·"2026-01-03T20:54:33.~~734977~~Z",	216	····················"iopub.execute_input":·"2024-12-01T16:18:22.161886Z",
217	····················"iopub.status.busy":·"2026-01-03T20:54:33.~~734720~~Z",	217	····················"iopub.status.busy":·"2024-12-01T16:18:22.161637Z",
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219	····················"shell.execute_reply":·"2026-01-03T20:54:33.~~763394~~Z"	219	····················"shell.execute_reply":·"2024-12-01T16:18:22.171457Z"
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_340240/427128218.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_3601275/427128218.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, 16 lines modified		Offset 126, 16 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_340240/427128218.py:3:·UserWarning:·set_ticklabels()·should~~·only~~	133	/tmp/ipykernel_3601275/427128218.py:3:·UserWarning:·set_ticklabels()·should
134	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.
141	[8]:	141	[8]:


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_3~~3678~~7/1205084488.py:18:·SyntaxWarning:·invalid·escape·sequence·'\$'	488	/tmp/ipykernel_3598977/1205084488.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_3~~3678~~7/1205084488.py:30:·SyntaxWarning:·invalid·escape·sequence·'\$'	490	/tmp/ipykernel_3598977/1205084488.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_3~~3678~~7/1205084488.py:18:·SyntaxWarning:·invalid·escape·sequence	244	/tmp/ipykernel_3598977/1205084488.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_3~~3678~~7/1205084488.py:30:·SyntaxWarning:·invalid·escape·sequence	247	/tmp/ipykernel_3598977/1205084488.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_3~~39947~~/3509132601.py:5:·SyntaxWarning:·invalid·escape·sequence·'\p'	181	/tmp/ipykernel_3600529/3509132601.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_3~~39947~~/3509132601.py:5:·SyntaxWarning:·invalid·escape·sequence·'\p'	183	/tmp/ipykernel_3600529/3509132601.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_3~~39947~~/3509132601.py:5:·SyntaxWarning:·invalid·escape·sequence	71	/tmp/ipykernel_3600529/3509132601.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_3~~39947~~/3509132601.py:5:·SyntaxWarning:·invalid·escape·sequence	75	/tmp/ipykernel_3600529/3509132601.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":·"2026-01-03T20:54:18.~~249017~~Z",	23	····················"iopub.execute_input":·"2024-12-01T16:18:11.330488Z",
24	····················"iopub.status.busy":·"2026-01-03T20:54:18.~~248742~~Z",	24	····················"iopub.status.busy":·"2024-12-01T16:18:11.330218Z",
25	····················"iopub.status.idle":·"2026-01-03T20:54:19.~~196871~~Z",	25	····················"iopub.status.idle":·"2024-12-01T16:18:11.824656Z",
26	····················"shell.execute_reply":·"2026-01-03T20:54:19.~~196169~~Z"	26	····················"shell.execute_reply":·"2024-12-01T16:18:11.824011Z"
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":·"2026-01-03T20:54:19.~~200066~~Z",	43	····················"iopub.execute_input":·"2024-12-01T16:18:11.827775Z",
44	····················"iopub.status.busy":·"2026-01-03T20:54:19.~~199692~~Z",	44	····················"iopub.status.busy":·"2024-12-01T16:18:11.827414Z",
45	····················"iopub.status.idle":·"2026-01-03T20:54:20.656~~179~~Z",	45	····················"iopub.status.idle":·"2024-12-01T16:18:13.316920Z",
46	····················"shell.execute_reply":·"2026-01-03T20:54:20.~~640~~201Z"	46	····················"shell.execute_reply":·"2024-12-01T16:18:13.316202Z"
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":·"2026-01-03T20:54:20.~~665163~~Z",	68	····················"iopub.execute_input":·"2024-12-01T16:18:13.341071Z",
69	····················"iopub.status.busy":·"2026-01-03T20:54:20.~~664744~~Z",	69	····················"iopub.status.busy":·"2024-12-01T16:18:13.340612Z",
70	····················"iopub.status.idle":·"2026-01-03T20:54:20.~~700235~~Z",	70	····················"iopub.status.idle":·"2024-12-01T16:18:13.348722Z",
71	····················"shell.execute_reply":·"2026-01-03T20:54:20.~~684150~~Z"	71	····················"shell.execute_reply":·"2024-12-01T16:18:13.348036Z"
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":·{
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Offset 125, 18 lines modified		Offset 125, 18 lines modified
125	········},	125	········},
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Offset 145, 18 lines modified		Offset 145, 18 lines modified
145	········},	145	········},
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149	············"metadata":·{	149	············"metadata":·{
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Offset 166, 18 lines modified		Offset 166, 18 lines modified
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