note 14 fix

DS-100 · Mar 27, 2024 · 214bfb9 · 214bfb9
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diff --git a/docs/feature_engineering/feature_engineering.html b/docs/feature_engineering/feature_engineering.html
@@ -360,7 +360,7 @@ <h3 data-number="14.1.1" class="anchored" data-anchor-id="gradient-descent-revie
 \\l(y, \hat{y}) &amp;= (y - \hat{y})^2
 \end{align}
 \]</span></p>
-<p>Plugging in <span class="math inline">\(f_{\vec{\theta}}(\vec{x})\)</span> for <span class="math inline">\(\hat{y}\)</span>, our loss function becomes <span class="math inline">\(l(\vec{\theta}, \vec{x}, \hat{y}) = (y_i - \theta_0x_0 - \theta_1x_1)^2\)</span>.</p>
+<p>Plugging in <span class="math inline">\(f_{\vec{\theta}}(\vec{x})\)</span> for <span class="math inline">\(\hat{y}\)</span>, our loss function becomes <span class="math inline">\(l(\vec{\theta}, \vec{x}, y_i) = (y_i - \theta_0x_0 - \theta_1x_1)^2\)</span>.</p>
 <p>To calculate our gradient vector, we can start by computing the partial derivative of the loss function with respect to <span class="math inline">\(\theta_0\)</span>: <span class="math display">\[\frac{\partial}{\partial \theta_{0}} l(\vec{\theta}, \vec{x}, y_i) = 2(y_i - \theta_0x_0 - \theta_1x_1)(-x_0)\]</span></p>
 <p>Let’s now do the same but with respect to <span class="math inline">\(\theta_1\)</span>: <span class="math display">\[\frac{\partial}{\partial \theta_{1}} l(\vec{\theta}, \vec{x}, y_i) = 2(y_i - \theta_0x_0 - \theta_1x_1)(-x_1)\]</span></p>
 <p>Putting this together, our gradient vector is: <span class="math display">\[\nabla_{\theta} l(\vec{\theta}, \vec{x}, y_i) =  \begin{bmatrix} -2(y_i - \theta_0x_0 - \theta_1x_1)(x_0) \\ -2(y_i - \theta_0x_0 - \theta_1x_1)(x_1) \end{bmatrix}\]</span></p>
@@ -1199,7 +1199,7 @@ <h2 data-number="14.7" class="anchored" data-anchor-id="bonus-stochastic-gradien
 <span id="cb8-78"><a href="#cb8-78" aria-hidden="true" tabindex="-1"></a>\end{align}</span>
 <span id="cb8-79"><a href="#cb8-79" aria-hidden="true" tabindex="-1"></a>$$</span>
 <span id="cb8-80"><a href="#cb8-80" aria-hidden="true" tabindex="-1"></a></span>
-<span id="cb8-81"><a href="#cb8-81" aria-hidden="true" tabindex="-1"></a>Plugging in $f_{\vec{\theta}}(\vec{x})$ for $\hat{y}$, our loss function becomes $l(\vec{\theta}, \vec{x}, \hat{y}) = (y_i - \theta_0x_0 - \theta_1x_1)^2$.</span>
+<span id="cb8-81"><a href="#cb8-81" aria-hidden="true" tabindex="-1"></a>Plugging in $f_{\vec{\theta}}(\vec{x})$ for $\hat{y}$, our loss function becomes $l(\vec{\theta}, \vec{x}, y_i) = (y_i - \theta_0x_0 - \theta_1x_1)^2$.</span>
 <span id="cb8-82"><a href="#cb8-82" aria-hidden="true" tabindex="-1"></a></span>
 <span id="cb8-83"><a href="#cb8-83" aria-hidden="true" tabindex="-1"></a>To calculate our gradient vector, we can start by computing the partial derivative of the loss function with respect to $\theta_0$: $$\frac{\partial}{\partial \theta_{0}} l(\vec{\theta}, \vec{x}, y_i) = 2(y_i - \theta_0x_0 - \theta_1x_1)(-x_0)$$</span>
 <span id="cb8-84"><a href="#cb8-84" aria-hidden="true" tabindex="-1"></a></span>

diff --git a/docs/gradient_descent/gradient_descent.html b/docs/gradient_descent/gradient_descent.html
diff --git a/docs/inference_causality/inference_causality_files/figure-pdf/cell-6-output-2.pdf b/docs/inference_causality/inference_causality_files/figure-pdf/cell-6-output-2.pdf
diff --git a/docs/inference_causality/inference_causality_files/figure-pdf/cell-8-output-1.pdf b/docs/inference_causality/inference_causality_files/figure-pdf/cell-8-output-1.pdf
diff --git a/docs/intro_to_modeling/intro_to_modeling_files/figure-html/cell-2-output-1.png b/docs/intro_to_modeling/intro_to_modeling_files/figure-html/cell-2-output-1.png
diff --git a/docs/pandas_2/pandas_2.html b/docs/pandas_2/pandas_2.html
@@ -1644,12 +1644,12 @@ <h3 data-number="3.3.4" class="anchored" data-anchor-id="sample"><span class="he
 </thead>
 <tbody>
 <tr class="odd">
-<td data-quarto-table-cell-role="th">67773</td>
+<td data-quarto-table-cell-role="th">322054</td>
 <td>CA</td>
-<td>F</td>
-<td>1973</td>
-<td>James</td>
-<td>35</td>
+<td>M</td>
+<td>1991</td>
+<td>Sherwin</td>
+<td>6</td>
 </tr>
 </tbody>
 </table>
@@ -1676,34 +1676,34 @@ <h3 data-number="3.3.4" class="anchored" data-anchor-id="sample"><span class="he
 </thead>
 <tbody>
 <tr class="odd">
-<td data-quarto-table-cell-role="th">166333</td>
-<td>2004</td>
-<td>Kimberli</td>
-<td>12</td>
+<td data-quarto-table-cell-role="th">348524</td>
+<td>2002</td>
+<td>Kenji</td>
+<td>17</td>
 </tr>
 <tr class="even">
-<td data-quarto-table-cell-role="th">35003</td>
-<td>1955</td>
-<td>Bianca</td>
-<td>11</td>
+<td data-quarto-table-cell-role="th">197715</td>
+<td>2012</td>
+<td>Rylee</td>
+<td>221</td>
 </tr>
 <tr class="odd">
-<td data-quarto-table-cell-role="th">388142</td>
-<td>2016</td>
-<td>Bernardo</td>
-<td>30</td>
+<td data-quarto-table-cell-role="th">239390</td>
+<td>2022</td>
+<td>Nahia</td>
+<td>5</td>
 </tr>
 <tr class="even">
-<td data-quarto-table-cell-role="th">35814</td>
-<td>1956</td>
-<td>Marsha</td>
-<td>175</td>
+<td data-quarto-table-cell-role="th">175096</td>
+<td>2006</td>
+<td>Rylin</td>
+<td>9</td>
 </tr>
 <tr class="odd">
-<td data-quarto-table-cell-role="th">327479</td>
-<td>1993</td>
-<td>Sandor</td>
-<td>5</td>
+<td data-quarto-table-cell-role="th">29180</td>
+<td>1951</td>
+<td>Pearl</td>
+<td>28</td>
 </tr>
 </tbody>
 </table>
@@ -1729,28 +1729,28 @@ <h3 data-number="3.3.4" class="anchored" data-anchor-id="sample"><span class="he
 </thead>
 <tbody>
 <tr class="odd">
-<td data-quarto-table-cell-role="th">150866</td>
+<td data-quarto-table-cell-role="th">150014</td>
 <td>2000</td>
-<td>Jakeline</td>
-<td>12</td>
+<td>Allyssa</td>
+<td>31</td>
 </tr>
 <tr class="even">
-<td data-quarto-table-cell-role="th">342578</td>
+<td data-quarto-table-cell-role="th">152815</td>
 <td>2000</td>
-<td>Alberto</td>
-<td>428</td>
+<td>Zahraa</td>
+<td>5</td>
 </tr>
 <tr class="odd">
-<td data-quarto-table-cell-role="th">150363</td>
+<td data-quarto-table-cell-role="th">342879</td>
 <td>2000</td>
-<td>Kaylene</td>
-<td>20</td>
+<td>Tucker</td>
+<td>63</td>
 </tr>
 <tr class="even">
-<td data-quarto-table-cell-role="th">149584</td>
+<td data-quarto-table-cell-role="th">344867</td>
 <td>2000</td>
-<td>Makenzie</td>
-<td>70</td>
+<td>Nery</td>
+<td>5</td>
 </tr>
 </tbody>
 </table>

diff --git a/docs/pandas_3/pandas_3.html b/docs/pandas_3/pandas_3.html
diff --git a/docs/regex/regex.html b/docs/regex/regex.html
@@ -680,11 +680,11 @@ <h4 data-number="6.2.1.2" class="anchored" data-anchor-id="canonicalization-with
 <span id="cb6-13"><a href="#cb6-13" aria-hidden="true" tabindex="-1"></a>county_and_state[<span class="st">'clean_county_pandas'</span>] <span class="op">=</span> canonicalize_county_series(county_and_state[<span class="st">'County'</span>])</span>
 <span id="cb6-14"><a href="#cb6-14" aria-hidden="true" tabindex="-1"></a>display(county_and_pop), display(county_and_state)<span class="op">;</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-stderr">
-<pre><code>/var/folders/7t/zbwy02ts2m7cn64fvwjqb8xw0000gp/T/ipykernel_24239/2523629438.py:3: FutureWarning:
+<pre><code>/var/folders/7t/zbwy02ts2m7cn64fvwjqb8xw0000gp/T/ipykernel_90453/2523629438.py:3: FutureWarning:
 
 The default value of regex will change from True to False in a future version. In addition, single character regular expressions will *not* be treated as literal strings when regex=True.
 
-/var/folders/7t/zbwy02ts2m7cn64fvwjqb8xw0000gp/T/ipykernel_24239/2523629438.py:3: FutureWarning:
+/var/folders/7t/zbwy02ts2m7cn64fvwjqb8xw0000gp/T/ipykernel_90453/2523629438.py:3: FutureWarning:
 
 The default value of regex will change from True to False in a future version. In addition, single character regular expressions will *not* be treated as literal strings when regex=True.
 </code></pre>

diff --git a/docs/sampling/sampling.html b/docs/sampling/sampling.html
@@ -698,7 +698,7 @@ <h4 data-number="9.3.3.3" class="anchored" data-anchor-id="simple-random-sample"
 <span id="cb13-2"><a href="#cb13-2" aria-hidden="true" tabindex="-1"></a>random_sample <span class="op">=</span> movie.sample(n, replace <span class="op">=</span> <span class="va">False</span>) <span class="co">## By default, replace = False</span></span>
 <span id="cb13-3"><a href="#cb13-3" aria-hidden="true" tabindex="-1"></a>np.mean(random_sample[<span class="st">"barbie"</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-display" data-execution_count="9">
-<pre><code>0.5295718371935135</code></pre>
+<pre><code>0.5302284944740621</code></pre>
 </div>
 </div>
 <p>This is very close to the actual vote of 0.5302792307692308!</p>
@@ -716,7 +716,7 @@ <h4 data-number="9.3.3.3" class="anchored" data-anchor-id="simple-random-sample"
 <span id="cb15-10"><a href="#cb15-10" aria-hidden="true" tabindex="-1"></a>Markdown(<span class="ss">f"**Actual** = </span><span class="sc">{</span>actual_barbie<span class="sc">:.4f}</span><span class="ss">, **Sample** = </span><span class="sc">{</span>sample_barbie<span class="sc">:.4f}</span><span class="ss">, "</span></span>
 <span id="cb15-11"><a href="#cb15-11" aria-hidden="true" tabindex="-1"></a>         <span class="ss">f"**Err** = </span><span class="sc">{</span><span class="dv">100</span><span class="op">*</span>err<span class="sc">:.2f}</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-display" data-execution_count="10">
-<p><strong>Actual</strong> = 0.5303, <strong>Sample</strong> = 0.5075, <strong>Err</strong> = 4.30%.</p>
+<p><strong>Actual</strong> = 0.5303, <strong>Sample</strong> = 0.5663, <strong>Err</strong> = 6.78%.</p>
 </div>
 </div>
 <p>We’ll learn how to choose this number when we (re)learn the Central Limit Theorem later in the semester.</p>
@@ -749,7 +749,7 @@ <h4 data-number="9.3.3.4" class="anchored" data-anchor-id="quantifying-chance-er
 <div class="sourceCode cell-code" id="cb18"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb18-1"><a href="#cb18-1" aria-hidden="true" tabindex="-1"></a>poll_result <span class="op">=</span> pd.Series(poll_result)</span>
 <span id="cb18-2"><a href="#cb18-2" aria-hidden="true" tabindex="-1"></a>np.<span class="bu">sum</span>(poll_result <span class="op">&gt;</span> <span class="fl">0.5</span>)<span class="op">/</span><span class="dv">1000</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-display" data-execution_count="13">
-<pre><code>0.957</code></pre>
+<pre><code>0.96</code></pre>
 </div>
 </div>
 <p>You can see the curve looks roughly Gaussian/normal. Using KDE:</p>

diff --git a/docs/sampling/sampling_files/figure-html/cell-13-output-1.png b/docs/sampling/sampling_files/figure-html/cell-13-output-1.png
diff --git a/docs/sampling/sampling_files/figure-html/cell-15-output-1.png b/docs/sampling/sampling_files/figure-html/cell-15-output-1.png
diff --git a/docs/visualization_2/visualization_2_files/figure-html/cell-17-output-2.png b/docs/visualization_2/visualization_2_files/figure-html/cell-17-output-2.png
diff --git a/feature_engineering/feature_engineering.qmd b/feature_engineering/feature_engineering.qmd
@@ -78,7 +78,7 @@ f_{\vec{\theta}}(\vec{x}) &= \vec{x}^T\vec{\theta} = \theta_0x_0 + \theta_1x_1
 \end{align}
 $$
 
-Plugging in $f_{\vec{\theta}}(\vec{x})$ for $\hat{y}$, our loss function becomes $l(\vec{\theta}, \vec{x}, \hat{y}) = (y_i - \theta_0x_0 - \theta_1x_1)^2$.
+Plugging in $f_{\vec{\theta}}(\vec{x})$ for $\hat{y}$, our loss function becomes $l(\vec{\theta}, \vec{x}, y_i) = (y_i - \theta_0x_0 - \theta_1x_1)^2$.
 
 To calculate our gradient vector, we can start by computing the partial derivative of the loss function with respect to $\theta_0$: $$\frac{\partial}{\partial \theta_{0}} l(\vec{\theta}, \vec{x}, y_i) = 2(y_i - \theta_0x_0 - \theta_1x_1)(-x_0)$$
 

diff --git a/index.log b/index.log
@@ -1,4 +1,4 @@
-This is XeTeX, Version 3.141592653-2.6-0.999995 (TeX Live 2023) (preloaded format=xelatex 2024.3.3)  21 MAR 2024 22:28
+This is XeTeX, Version 3.141592653-2.6-0.999995 (TeX Live 2023) (preloaded format=xelatex 2024.3.3)  27 MAR 2024 15:03
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  restricted \write18 enabled.
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diff --git a/index.pdf b/index.pdf