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56 changes: 28 additions & 28 deletions 10_Residuals.html

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8 changes: 4 additions & 4 deletions 11_Inference.html
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Expand Down Expand Up @@ -1085,7 +1085,7 @@ <h3>信頼区間の図示<a class="headerlink" href="#id9" title="Link to this h
</div>
</div>
<div class="cell_output docutils container">
<img alt="_images/5643148905b90256352381999348f9bcc390317c231a6fd7d3860b641059d250.png" src="_images/5643148905b90256352381999348f9bcc390317c231a6fd7d3860b641059d250.png" />
<img alt="_images/ac0e3d823265fd88f08c32edce99c77ed51cb53ee7ee49ab15047011b9978485.png" src="_images/ac0e3d823265fd88f08c32edce99c77ed51cb53ee7ee49ab15047011b9978485.png" />
</div>
</div>
<p><code class="docutils literal notranslate"><span class="pre">ACT</span></code>の信頼区間に<code class="docutils literal notranslate"><span class="pre">0</span></code>が含まれることが分かる。</p>
Expand Down Expand Up @@ -1402,8 +1402,8 @@ <h4>例2<a class="headerlink" href="#id15" title="Link to this heading">#</a><
Dep. Variable: np.log(salary) R-squared: 0.628
Model: OLS Adj. R-squared: 0.622
Method: Least Squares F-statistic: 117.1
Date: Sun, 21 Jul 2024 Prob (F-statistic): 2.94e-72
Time: 23:00:17 Log-Likelihood: -385.11
Date: Sat, 10 Aug 2024 Prob (F-statistic): 2.94e-72
Time: 04:34:16 Log-Likelihood: -385.11
No. Observations: 353 AIC: 782.2
Df Residuals: 347 BIC: 805.4
Df Model: 5
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47 changes: 22 additions & 25 deletions 12_Asymptotics.html
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Expand Down Expand Up @@ -626,8 +626,8 @@ <h4>誤差項のプロット<a class="headerlink" href="#id5" title="Link to thi
</div>
</div>
<div class="cell_output docutils container">
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>array([-0.35440262, -0.4135089 , -0.01572952, -0.68708681, -0.63373862,
0.52938341, 1.23926651, -0.02076896, -0.49073671, -0.06817554])
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>array([-0.57527126, -0.40252697, -0.63543846, -0.66212078, 0.74823649,
-0.58274413, -0.57411454, -0.24486782, 0.51825711, -0.3612924 ])
</pre></div>
</div>
</div>
Expand All @@ -644,7 +644,7 @@ <h4>誤差項のプロット<a class="headerlink" href="#id5" title="Link to thi
</div>
</div>
<div class="cell_output docutils container">
<img alt="_images/928d4125376b06848df7f6e8da0b5b39992eb9a65c49bb0906c3025f9bcd3fd3.png" src="_images/928d4125376b06848df7f6e8da0b5b39992eb9a65c49bb0906c3025f9bcd3fd3.png" />
<img alt="_images/c920ab039ad2567efccac73576433ed9435bee1d69bb56e3b42ca504e2e30230.png" src="_images/c920ab039ad2567efccac73576433ed9435bee1d69bb56e3b42ca504e2e30230.png" />
</div>
</div>
<p>確認のために、生成された<code class="docutils literal notranslate"><span class="pre">n</span></code>個のランダム変数(誤差項)の平均を計算してみる。</p>
Expand All @@ -655,7 +655,7 @@ <h4>誤差項のプロット<a class="headerlink" href="#id5" title="Link to thi
</div>
</div>
<div class="cell_output docutils container">
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>-0.008538444292774418
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>-0.024132954826839456
</pre></div>
</div>
</div>
Expand Down Expand Up @@ -767,8 +767,8 @@ <h4>一致性<a class="headerlink" href="#id6" title="Link to this heading">#</a
</div>
</div>
<div class="cell_output docutils container">
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>array([ 0.92353502, 0.25779507, 1.05438918, ..., 0.33071448,
-0.27047218, 0.59614436])
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>array([0.1332395 , 0.16832287, 1.08112139, ..., 0.13790435, 0.21333293,
0.65723774])
</pre></div>
</div>
</div>
Expand Down Expand Up @@ -806,7 +806,7 @@ <h4>一致性<a class="headerlink" href="#id6" title="Link to this heading">#</a
</div>
</div>
<div class="cell_output docutils container">
<img alt="_images/2c4ad099ce7cd581989ef670f6fb7e150c8f81e2e8e9cc68c404825f0ca744e5.png" src="_images/2c4ad099ce7cd581989ef670f6fb7e150c8f81e2e8e9cc68c404825f0ca744e5.png" />
<img alt="_images/6846451fed28a65997c65e33dcbe0acdcfb7b683e98fe2af7a7311eb55156abd.png" src="_images/6846451fed28a65997c65e33dcbe0acdcfb7b683e98fe2af7a7311eb55156abd.png" />
</div>
</div>
<p>上のコードには同じような行が複数あり,単純な間違いの可能性が高くなる。。<code class="docutils literal notranslate"><span class="pre">for</span></code>ループを使うとよりコンパクトに書くことが可能となり,間違いも少なくなる。</p>
Expand Down Expand Up @@ -838,7 +838,7 @@ <h4>一致性<a class="headerlink" href="#id6" title="Link to this heading">#</a
</div>
</div>
<div class="cell_output docutils container">
<img alt="_images/2c4ad099ce7cd581989ef670f6fb7e150c8f81e2e8e9cc68c404825f0ca744e5.png" src="_images/2c4ad099ce7cd581989ef670f6fb7e150c8f81e2e8e9cc68c404825f0ca744e5.png" />
<img alt="_images/6846451fed28a65997c65e33dcbe0acdcfb7b683e98fe2af7a7311eb55156abd.png" src="_images/6846451fed28a65997c65e33dcbe0acdcfb7b683e98fe2af7a7311eb55156abd.png" />
</div>
</div>
<p><コードの説明></p>
Expand Down Expand Up @@ -1043,7 +1043,7 @@ <h3>誤差項の正規性が満たされる場合<a class="headerlink" href="#id
</div>
</div>
<div class="cell_output docutils container">
<img alt="_images/790f7340a57c4f307e5bca5cca2d96bd03ed29abd5528da56a82b39ed8a3ff59.png" src="_images/790f7340a57c4f307e5bca5cca2d96bd03ed29abd5528da56a82b39ed8a3ff59.png" />
<img alt="_images/12b5d80f5e15c2c55090f1c6f9833105cc53517849a11c8f9111133f4b23c362.png" src="_images/12b5d80f5e15c2c55090f1c6f9833105cc53517849a11c8f9111133f4b23c362.png" />
</div>
</div>
<p>(結果:小標本特性)</p>
Expand Down Expand Up @@ -1143,7 +1143,7 @@ <h3>誤差項の正規性が満たされない場合<a class="headerlink" href="
</div>
</div>
<div class="cell_output docutils container">
<img alt="_images/d8237a81ebe4dfc6313c3f9b7bcfe47f391e8c02cc32db9988d10f54845c04f0.png" src="_images/d8237a81ebe4dfc6313c3f9b7bcfe47f391e8c02cc32db9988d10f54845c04f0.png" />
<img alt="_images/50b9b05af570926fe699d6304fd71bd3267c3ec9b5c0651fc269f878ef34f4a6.png" src="_images/50b9b05af570926fe699d6304fd71bd3267c3ec9b5c0651fc269f878ef34f4a6.png" />
</div>
</div>
<p>(結果:大標本特性)</p>
Expand Down Expand Up @@ -1172,7 +1172,7 @@ <h3>qqプロット<a class="headerlink" href="#qq" title="Link to this heading">
</div>
</div>
<div class="cell_output docutils container">
<img alt="_images/304e312a33e33bc6cb9257ef682ba342076a55154a915dd0caab54ebf9713e5a.png" src="_images/304e312a33e33bc6cb9257ef682ba342076a55154a915dd0caab54ebf9713e5a.png" />
<img alt="_images/f04220d1380d0a6c148f8941371fbfbd50dbf5cdabe27baf261600b50254d405.png" src="_images/f04220d1380d0a6c148f8941371fbfbd50dbf5cdabe27baf261600b50254d405.png" />
</div>
</div>
<p><strong>一様分布</strong>から生成したデータの場合。45度線から乖離しているのが分かる。</p>
Expand All @@ -1185,7 +1185,7 @@ <h3>qqプロット<a class="headerlink" href="#qq" title="Link to this heading">
</div>
</div>
<div class="cell_output docutils container">
<img alt="_images/c6ad2a9ba116b380ca7c5c759eb0a0271fb573be39aa66025fbe53311bc392f2.png" src="_images/c6ad2a9ba116b380ca7c5c759eb0a0271fb573be39aa66025fbe53311bc392f2.png" />
<img alt="_images/4904e7c3760eaa255ad5392eff5e9bb37f58922e8de9f3838007b187c7fcbd45.png" src="_images/4904e7c3760eaa255ad5392eff5e9bb37f58922e8de9f3838007b187c7fcbd45.png" />
</div>
</div>
<p><code class="docutils literal notranslate"><span class="pre">wooldridge</span></code>パッケージにある<code class="docutils literal notranslate"><span class="pre">wage1</span></code>のデータを使ってみる。</p>
Expand All @@ -1201,7 +1201,7 @@ <h3>qqプロット<a class="headerlink" href="#qq" title="Link to this heading">
</div>
</div>
<div class="cell_output docutils container">
<img alt="_images/fe88f1288ffd20e6163c42013cc07f8181f03c98d18f861e7c6375b65734b4b0.png" src="_images/fe88f1288ffd20e6163c42013cc07f8181f03c98d18f861e7c6375b65734b4b0.png" />
<img alt="_images/879e9c27b407a454f2f21cc4da812b9269cf6b496d90d551162ec9cacef2e9e8.png" src="_images/879e9c27b407a454f2f21cc4da812b9269cf6b496d90d551162ec9cacef2e9e8.png" />
</div>
</div>
<p>被説明変数の<code class="docutils literal notranslate"><span class="pre">wage</span></code>に対数を取ると、こちらの方が当てはまりが良いことが分かる。</p>
Expand All @@ -1216,7 +1216,7 @@ <h3>qqプロット<a class="headerlink" href="#qq" title="Link to this heading">
</div>
</div>
<div class="cell_output docutils container">
<img alt="_images/d17100062743837002f32f7295c061981b213f2d712d7803120c56758bb31a62.png" src="_images/d17100062743837002f32f7295c061981b213f2d712d7803120c56758bb31a62.png" />
<img alt="_images/090f612db09212adbecc6976ad86129ae282ffb432feb308e00aaa8dc07e307c.png" src="_images/090f612db09212adbecc6976ad86129ae282ffb432feb308e00aaa8dc07e307c.png" />
</div>
</div>
</section>
Expand All @@ -1239,10 +1239,7 @@ <h3>Jarque-Bera検定<a class="headerlink" href="#jarque-bera" title="Link to th
</div>
</div>
<div class="cell_output docutils container">
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>(0.8281366633673981,
0.6609557855011297,
-0.06669583925118651,
3.1481796880410897)
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>(2.907472419356873, 0.233695519490203, -0.18639675364837652, 2.975840590931986)
</pre></div>
</div>
</div>
Expand All @@ -1265,10 +1262,10 @@ <h3>Jarque-Bera検定<a class="headerlink" href="#jarque-bera" title="Link to th
</div>
</div>
<div class="cell_output docutils container">
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>(32.296249575492546,
9.704172582947033e-08,
0.10335504110131778,
1.7722007812596468)
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>(28.272041303106743,
7.257787275594346e-07,
-0.03686693505400198,
1.8374075095081597)
</pre></div>
</div>
</div>
Expand Down Expand Up @@ -1350,7 +1347,7 @@ <h3>Omnibus検定<a class="headerlink" href="#omnibus" title="Link to this headi
</div>
</div>
<div class="cell_output docutils container">
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>NormaltestResult(statistic=1.0258339622496038, pvalue=0.5987464968031593)
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>NormaltestResult(statistic=2.9335817364028314, pvalue=0.23066453158693587)
</pre></div>
</div>
</div>
Expand All @@ -1366,7 +1363,7 @@ <h3>Omnibus検定<a class="headerlink" href="#omnibus" title="Link to this headi
</div>
</div>
<div class="cell_output docutils container">
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>NormaltestResult(statistic=390.2161138814273, pvalue=1.843518481342668e-85)
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>NormaltestResult(statistic=246.09309230429423, pvalue=3.6438793496443564e-54)
</pre></div>
</div>
</div>
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Expand Down Expand Up @@ -740,7 +740,7 @@ <h3>不均一分散頑健推定:方法1<a class="headerlink" href="#id3" tit
</div>
</div>
<div class="cell_output docutils container">
<img alt="_images/20942f17555278671f81ceed8052613c7fdba9b4b8425fe2a915f5d364e461cc.png" src="_images/20942f17555278671f81ceed8052613c7fdba9b4b8425fe2a915f5d364e461cc.png" />
<img alt="_images/bb5bc110f30ca3561a1ee5dc8a356f7fcba40a135ee4ec3b276a514fdb8fb620.png" src="_images/bb5bc110f30ca3561a1ee5dc8a356f7fcba40a135ee4ec3b276a514fdb8fb620.png" />
</div>
</div>
<p>2つ目の方法は<code class="docutils literal notranslate"><span class="pre">plt.plot()</span></code>を使う。オップション<code class="docutils literal notranslate"><span class="pre">'o'</span></code>はマーカの指定である。</p>
Expand All @@ -752,7 +752,7 @@ <h3>不均一分散頑健推定:方法1<a class="headerlink" href="#id3" tit
</div>
</div>
<div class="cell_output docutils container">
<img alt="_images/20942f17555278671f81ceed8052613c7fdba9b4b8425fe2a915f5d364e461cc.png" src="_images/20942f17555278671f81ceed8052613c7fdba9b4b8425fe2a915f5d364e461cc.png" />
<img alt="_images/bb5bc110f30ca3561a1ee5dc8a356f7fcba40a135ee4ec3b276a514fdb8fb620.png" src="_images/bb5bc110f30ca3561a1ee5dc8a356f7fcba40a135ee4ec3b276a514fdb8fb620.png" />
</div>
</div>
<p>3つ目は<code class="docutils literal notranslate"><span class="pre">scatter()</span></code>を使う。<code class="docutils literal notranslate"><span class="pre">.index</span></code><code class="docutils literal notranslate"><span class="pre">res_ols.resd</span></code>の属性でインデックスを示す。</p>
Expand All @@ -764,7 +764,7 @@ <h3>不均一分散頑健推定:方法1<a class="headerlink" href="#id3" tit
</div>
</div>
<div class="cell_output docutils container">
<img alt="_images/20942f17555278671f81ceed8052613c7fdba9b4b8425fe2a915f5d364e461cc.png" src="_images/20942f17555278671f81ceed8052613c7fdba9b4b8425fe2a915f5d364e461cc.png" />
<img alt="_images/bb5bc110f30ca3561a1ee5dc8a356f7fcba40a135ee4ec3b276a514fdb8fb620.png" src="_images/bb5bc110f30ca3561a1ee5dc8a356f7fcba40a135ee4ec3b276a514fdb8fb620.png" />
</div>
</div>
</section>
Expand Down Expand Up @@ -1088,7 +1088,7 @@ <h3><code class="docutils literal notranslate"><span class="pre">lmdiag</span></
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;Figure size 800x700 with 0 Axes&gt;
</pre></div>
</div>
<img alt="_images/88581bb6fd5e0a9bff6d9d8dc92914d1e6d830062ddf2bb75aef0c4fbdfce48d.png" src="_images/88581bb6fd5e0a9bff6d9d8dc92914d1e6d830062ddf2bb75aef0c4fbdfce48d.png" />
<img alt="_images/93709a61c9839227475de6b792c36ca3f0c2077d0964135af6ec1d8f1b1bcf37.png" src="_images/93709a61c9839227475de6b792c36ca3f0c2077d0964135af6ec1d8f1b1bcf37.png" />
</div>
</div>
<p>対数変換後</p>
Expand All @@ -1104,7 +1104,7 @@ <h3><code class="docutils literal notranslate"><span class="pre">lmdiag</span></
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;Figure size 800x700 with 0 Axes&gt;
</pre></div>
</div>
<img alt="_images/7fe232696eb2c0b315ab588ad6514b00a2f241e8fb0354b2521e7bf33e975394.png" src="_images/7fe232696eb2c0b315ab588ad6514b00a2f241e8fb0354b2521e7bf33e975394.png" />
<img alt="_images/aebe0a2a2a95c4f32a65e6d631cba479e7318bd42bb211ef10487d1364686f40.png" src="_images/aebe0a2a2a95c4f32a65e6d631cba479e7318bd42bb211ef10487d1364686f40.png" />
</div>
</div>
<p>対数変換により残差の変化がより均一的になり,Residuals vs. LeverageのCook’s Distanceを見ても外れ値がなくなっている。</p>
Expand All @@ -1120,7 +1120,7 @@ <h3><code class="docutils literal notranslate"><span class="pre">Matplotlib</spa
</div>
</div>
<div class="cell_output docutils container">
<img alt="_images/81ee5a4aed90697970b311a45e1498926581a8b7af66fc9946cfb0b23e6ca6b3.png" src="_images/81ee5a4aed90697970b311a45e1498926581a8b7af66fc9946cfb0b23e6ca6b3.png" />
<img alt="_images/546b8764e53c3f80e2714774fbfa8e8c945cf65656d90ff33ddcd7046b9ab7d6.png" src="_images/546b8764e53c3f80e2714774fbfa8e8c945cf65656d90ff33ddcd7046b9ab7d6.png" />
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<p>対数変換後</p>
Expand All @@ -1132,7 +1132,7 @@ <h3><code class="docutils literal notranslate"><span class="pre">Matplotlib</spa
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<div class="cell_output docutils container">
<img alt="_images/8f46d8c13373dbe966d64f30ad285ce2510df2b78bc041f6afc6efeda905bf05.png" src="_images/8f46d8c13373dbe966d64f30ad285ce2510df2b78bc041f6afc6efeda905bf05.png" />
<img alt="_images/8e6ba9a68c7796833cd47e325fbc466d78172e50ea842150cab748ba905557c3.png" src="_images/8e6ba9a68c7796833cd47e325fbc466d78172e50ea842150cab748ba905557c3.png" />
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<p>対数変換により残差の変化がより均一的になったのが確認できる。</p>
Expand Down Expand Up @@ -1169,7 +1169,7 @@ <h3><code class="docutils literal notranslate"><span class="pre">seaborn</span><
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<img alt="_images/b65543aab013e9db4f91a9b8cea03c4e85a11d5196067ff06c3bcfb7b2dd7003.png" src="_images/b65543aab013e9db4f91a9b8cea03c4e85a11d5196067ff06c3bcfb7b2dd7003.png" />
<img alt="_images/5fc10e8247190e809aba222949b2cd3725840b13af654bb772749e4a1f43b995.png" src="_images/5fc10e8247190e809aba222949b2cd3725840b13af654bb772749e4a1f43b995.png" />
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<p>対数変換後</p>
Expand All @@ -1181,7 +1181,7 @@ <h3><code class="docutils literal notranslate"><span class="pre">seaborn</span><
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</div>
<div class="cell_output docutils container">
<img alt="_images/e1ff89962e4c37c8a79760268c455fe2a0493eed911fa5d0d67a947939ed7437.png" src="_images/e1ff89962e4c37c8a79760268c455fe2a0493eed911fa5d0d67a947939ed7437.png" />
<img alt="_images/04cc094df93956e2a6985b9ae227259d5fd5043647de4d46f2d9ace86134e9ce.png" src="_images/04cc094df93956e2a6985b9ae227259d5fd5043647de4d46f2d9ace86134e9ce.png" />
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