publish random var notes

_quarto.yml

@@ -32,7 +32,7 @@ book:
         - feature_engineering/feature_engineering.qmd
         - case_study_HCE/case_study_HCE.qmd
         - cv_regularization/cv_reg.qmd
-        # - probability_1/probability_1.qmd
+        - probability_1/probability_1.qmd
         # - probability_2/probability_2.qmd
         # - case_study_climate/case_study_climate.qmd
         # - inference_causality/inference_causality.qmd

docs/case_study_HCE/case_study_HCE.html

@@ -242,6 +242,12 @@
   <a href="../cv_regularization/cv_reg.html" class="sidebar-item-text sidebar-link">
  <span class="menu-text"><span class="chapter-number">16</span>&nbsp; <span class="chapter-title">Cross Validation and Regularization</span></span></a>
   </div>
+</li>
+        <li class="sidebar-item">
+  <div class="sidebar-item-container"> 
+  <a href="../probability_1/probability_1.html" class="sidebar-item-text sidebar-link">
+ <span class="menu-text"><span class="chapter-number">17</span>&nbsp; <span class="chapter-title">Random Variables</span></span></a>
+  </div>
 </li>
     </ul>
     </div>

docs/constant_model_loss_transformations/loss_transformations.html

@@ -244,6 +244,12 @@
   <a href="../cv_regularization/cv_reg.html" class="sidebar-item-text sidebar-link">
  <span class="menu-text"><span class="chapter-number">16</span>&nbsp; <span class="chapter-title">Cross Validation and Regularization</span></span></a>
   </div>
+</li>
+        <li class="sidebar-item">
+  <div class="sidebar-item-container"> 
+  <a href="../probability_1/probability_1.html" class="sidebar-item-text sidebar-link">
+ <span class="menu-text"><span class="chapter-number">17</span>&nbsp; <span class="chapter-title">Random Variables</span></span></a>
+  </div>
 </li>
     </ul>
     </div>

docs/cv_regularization/cv_reg.html

@@ -64,6 +64,7 @@
 <script src="../site_libs/quarto-search/fuse.min.js"></script>
 <script src="../site_libs/quarto-search/quarto-search.js"></script>
 <meta name="quarto:offset" content="../">
+<link href="../probability_1/probability_1.html" rel="next">
 <link href="../case_study_HCE/case_study_HCE.html" rel="prev">
 <link href="../data100_logo.png" rel="icon" type="image/png">
 <script src="../site_libs/quarto-html/quarto.js"></script>
@@ -246,6 +247,12 @@
   <a href="../cv_regularization/cv_reg.html" class="sidebar-item-text sidebar-link active">
  <span class="menu-text"><span class="chapter-number">16</span>&nbsp; <span class="chapter-title">Cross Validation and Regularization</span></span></a>
   </div>
+</li>
+        <li class="sidebar-item">
+  <div class="sidebar-item-container"> 
+  <a href="../probability_1/probability_1.html" class="sidebar-item-text sidebar-link">
+ <span class="menu-text"><span class="chapter-number">17</span>&nbsp; <span class="chapter-title">Random Variables</span></span></a>
+  </div>
 </li>
     </ul>
     </div>
@@ -689,7 +696,7 @@ <h2 data-number="16.6" class="anchored" data-anchor-id="l2-ridge-regularization"
 <span id="cb9-3"><a href="#cb9-3" aria-hidden="true" tabindex="-1"></a></span>
 <span id="cb9-4"><a href="#cb9-4" aria-hidden="true" tabindex="-1"></a>ridge_model.coef_</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-display" data-execution_count="7">
-<pre><code>array([ 5.89130559e-02, -6.42445915e-03,  4.44468157e-05, -8.83981945e-08])</code></pre>
+<pre><code>array([ 5.89130560e-02, -6.42445916e-03,  4.44468157e-05, -8.83981945e-08])</code></pre>
 </div>
 </div>
 </section>
@@ -987,6 +994,9 @@ <h2 data-number="16.7" class="anchored" data-anchor-id="regression-summary"><spa
       </a>          
   </div>
   <div class="nav-page nav-page-next">
+      <a href="../probability_1/probability_1.html" class="pagination-link">
+        <span class="nav-page-text"><span class="chapter-number">17</span>&nbsp; <span class="chapter-title">Random Variables</span></span> <i class="bi bi-arrow-right-short"></i>
+      </a>
   </div>
 </nav>
 </div> <!-- /content -->

docs/feature_engineering/feature_engineering.html

@@ -247,6 +247,12 @@
   <a href="../cv_regularization/cv_reg.html" class="sidebar-item-text sidebar-link">
  <span class="menu-text"><span class="chapter-number">16</span>&nbsp; <span class="chapter-title">Cross Validation and Regularization</span></span></a>
   </div>
+</li>
+        <li class="sidebar-item">
+  <div class="sidebar-item-container"> 
+  <a href="../probability_1/probability_1.html" class="sidebar-item-text sidebar-link">
+ <span class="menu-text"><span class="chapter-number">17</span>&nbsp; <span class="chapter-title">Random Variables</span></span></a>
+  </div>
 </li>
     </ul>
     </div>
@@ -520,7 +526,7 @@ <h2 data-number="14.2" class="anchored" data-anchor-id="sklearn"><span class="he
 <span id="cb11-4"><a href="#cb11-4" aria-hidden="true" tabindex="-1"></a></span>
 <span id="cb11-5"><a href="#cb11-5" aria-hidden="true" tabindex="-1"></a>my_model.fit(X, Y)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-display" data-execution_count="6">
-<style>#sk-container-id-1 {color: black;}#sk-container-id-1 pre{padding: 0;}#sk-container-id-1 div.sk-toggleable {background-color: white;}#sk-container-id-1 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-1 label.sk-toggleable__label-arrow:before {content: "▸";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-1 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-1 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-1 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: "▾";}#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-1 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-1 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-1 div.sk-parallel-item::after {content: "";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-serial::before {content: "";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-1 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-1 div.sk-item {position: relative;z-index: 1;}#sk-container-id-1 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-1 div.sk-item::before, #sk-container-id-1 div.sk-parallel-item::before {content: "";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-1 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-1 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-1 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-1 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-1 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-1 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-1 div.sk-label-container {text-align: center;}#sk-container-id-1 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-1 div.sk-text-repr-fallback {display: none;}</style><div id="sk-container-id-1" class="sk-top-container"><div class="sk-text-repr-fallback"><pre>LinearRegression()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br>On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class="sk-container" hidden=""><div class="sk-item"><div class="sk-estimator sk-toggleable"><input class="sk-toggleable__control sk-hidden--visually" id="sk-estimator-id-1" type="checkbox" checked=""><label for="sk-estimator-id-1" class="sk-toggleable__label sk-toggleable__label-arrow">LinearRegression</label><div class="sk-toggleable__content"><pre>LinearRegression()</pre></div></div></div></div></div>
+<style>#sk-container-id-1 {color: black;background-color: white;}#sk-container-id-1 pre{padding: 0;}#sk-container-id-1 div.sk-toggleable {background-color: white;}#sk-container-id-1 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-1 label.sk-toggleable__label-arrow:before {content: "▸";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-1 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-1 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-1 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: "▾";}#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-1 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-1 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-1 div.sk-parallel-item::after {content: "";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-serial::before {content: "";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-1 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-1 div.sk-item {position: relative;z-index: 1;}#sk-container-id-1 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-1 div.sk-item::before, #sk-container-id-1 div.sk-parallel-item::before {content: "";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-1 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-1 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-1 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-1 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-1 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-1 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-1 div.sk-label-container {text-align: center;}#sk-container-id-1 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-1 div.sk-text-repr-fallback {display: none;}</style><div id="sk-container-id-1" class="sk-top-container"><div class="sk-text-repr-fallback"><pre>LinearRegression()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br>On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class="sk-container" hidden=""><div class="sk-item"><div class="sk-estimator sk-toggleable"><input class="sk-toggleable__control sk-hidden--visually" id="sk-estimator-id-1" type="checkbox" checked=""><label for="sk-estimator-id-1" class="sk-toggleable__label sk-toggleable__label-arrow">LinearRegression</label><div class="sk-toggleable__content"><pre>LinearRegression()</pre></div></div></div></div></div>
 </div>
 </div>
 <p>Notice that we use <strong>double brackets</strong> to extract this column. Why double brackets instead of just single brackets? The <code>.fit</code> method, by default, expects to receive <strong>2-dimensional</strong> data – some kind of data that includes both rows and columns. Writing <code>penguins["flipper_length_mm"]</code> would return a 1D <code>Series</code>, causing <code>sklearn</code> to error. We avoid this by writing <code>penguins[["flipper_length_mm"]]</code> to produce a 2D <code>DataFrame</code>.</p>
@@ -571,7 +577,7 @@ <h2 data-number="14.2" class="anchored" data-anchor-id="sklearn"><span class="he
 <span id="cb18-12"><a href="#cb18-12" aria-hidden="true" tabindex="-1"></a></span>
 <span id="cb18-13"><a href="#cb18-13" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="ss">f"The RMSE of the model is </span><span class="sc">{</span>np<span class="sc">.</span>sqrt(np.mean((Y<span class="op">-</span>Y_hat_two_features)<span class="op">**</span><span class="dv">2</span>))<span class="sc">}</span><span class="ss">"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
-<pre><code>The RMSE of the model is 0.9881331104079044</code></pre>
+<pre><code>The RMSE of the model is 0.9881331104079045</code></pre>
 </div>
 </div>
 <p>We can also see that we obtain the same predictions using <code>sklearn</code> as we did when applying the ordinary least squares formula before!</p>
@@ -941,7 +947,7 @@ <h2 data-number="14.6" class="anchored" data-anchor-id="polynomial-features"><sp
 <span id="cb26-12"><a href="#cb26-12" aria-hidden="true" tabindex="-1"></a></span>
 <span id="cb26-13"><a href="#cb26-13" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="ss">f"MSE of model with (hp^2) feature: </span><span class="sc">{</span>np<span class="sc">.</span>mean((Y<span class="op">-</span>hp2_model_predictions)<span class="op">**</span><span class="dv">2</span>)<span class="sc">}</span><span class="ss">"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
-<pre><code>MSE of model with (hp^2) feature: 18.984768907617223</code></pre>
+<pre><code>MSE of model with (hp^2) feature: 18.984768907617216</code></pre>
 </div>
 <div class="cell-output cell-output-display">
 <p><img src="feature_engineering_files/figure-html/cell-17-output-2.png" width="585" height="429"></p>

docs/index.html

@@ -215,6 +215,12 @@
   <a href="./cv_regularization/cv_reg.html" class="sidebar-item-text sidebar-link">
  <span class="menu-text"><span class="chapter-number">16</span>&nbsp; <span class="chapter-title">Cross Validation and Regularization</span></span></a>
   </div>
+</li>
+        <li class="sidebar-item">
+  <div class="sidebar-item-container"> 
+  <a href="./probability_1/probability_1.html" class="sidebar-item-text sidebar-link">
+ <span class="menu-text"><span class="chapter-number">17</span>&nbsp; <span class="chapter-title">Random Variables</span></span></a>
+  </div>
 </li>
     </ul>
     </div>

docs/intro_lec/introduction.html

@@ -208,6 +208,12 @@
   <a href="../cv_regularization/cv_reg.html" class="sidebar-item-text sidebar-link">
  <span class="menu-text"><span class="chapter-number">16</span>&nbsp; <span class="chapter-title">Cross Validation and Regularization</span></span></a>
   </div>
+</li>
+        <li class="sidebar-item">
+  <div class="sidebar-item-container"> 
+  <a href="../probability_1/probability_1.html" class="sidebar-item-text sidebar-link">
+ <span class="menu-text"><span class="chapter-number">17</span>&nbsp; <span class="chapter-title">Random Variables</span></span></a>
+  </div>
 </li>
     </ul>
     </div>

docs/intro_to_modeling/intro_to_modeling.html

@@ -244,6 +244,12 @@
   <a href="../cv_regularization/cv_reg.html" class="sidebar-item-text sidebar-link">
  <span class="menu-text"><span class="chapter-number">16</span>&nbsp; <span class="chapter-title">Cross Validation and Regularization</span></span></a>
   </div>
+</li>
+        <li class="sidebar-item">
+  <div class="sidebar-item-container"> 
+  <a href="../probability_1/probability_1.html" class="sidebar-item-text sidebar-link">
+ <span class="menu-text"><span class="chapter-number">17</span>&nbsp; <span class="chapter-title">Random Variables</span></span></a>
+  </div>
 </li>
     </ul>
     </div>

docs/ols/ols.html

@@ -247,6 +247,12 @@
   <a href="../cv_regularization/cv_reg.html" class="sidebar-item-text sidebar-link">
  <span class="menu-text"><span class="chapter-number">16</span>&nbsp; <span class="chapter-title">Cross Validation and Regularization</span></span></a>
   </div>
+</li>
+        <li class="sidebar-item">
+  <div class="sidebar-item-container"> 
+  <a href="../probability_1/probability_1.html" class="sidebar-item-text sidebar-link">
+ <span class="menu-text"><span class="chapter-number">17</span>&nbsp; <span class="chapter-title">Random Variables</span></span></a>
+  </div>
 </li>
     </ul>
     </div>

docs/pandas_1/pandas_1.html

@@ -247,6 +247,12 @@
   <a href="../cv_regularization/cv_reg.html" class="sidebar-item-text sidebar-link">
  <span class="menu-text"><span class="chapter-number">16</span>&nbsp; <span class="chapter-title">Cross Validation and Regularization</span></span></a>
   </div>
+</li>
+        <li class="sidebar-item">
+  <div class="sidebar-item-container"> 
+  <a href="../probability_1/probability_1.html" class="sidebar-item-text sidebar-link">
+ <span class="menu-text"><span class="chapter-number">17</span>&nbsp; <span class="chapter-title">Random Variables</span></span></a>
+  </div>
 </li>
     </ul>
     </div>