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6 changes: 3 additions & 3 deletions constant_model_loss_transformations/loss_transformations.qmd
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Expand Up @@ -822,11 +822,11 @@ In this calculation, we use the fact that the **sum of deviations from the mean
Let's quickly walk through the proof for this:
$$\sum_{i=1}^{n} (y_i - \bar{y}) = \sum_{i=1}^{n} y_i - \sum_{i=1}^{n} \bar{y}$$

$$ = \sum\_{i=1}^{n} y_i - n\bar{y}$$
$$ = \sum_{i=1}^{n} y_i - n\bar{y}$$

$$ = \sum*{i=1}^{n} y_i - n\frac{1}{n}\sum*{i=1}^{n}y$$
$$ = \sum_{i=1}^{n} y_i - n\frac{1}{n}\sum_{i=1}^{n}y$$

$$ = \sum*{i=1}^{n} y_i - \sum*{i=1}^{n}y_i$$
$$ = \sum_{i=1}^{n} y_i - \sum_{i=1}^{n}y_i$$

In our calculations, we'll also be using the definition of the variance as a sample. As a refresher:

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12 changes: 6 additions & 6 deletions docs/constant_model_loss_transformations/loss_transformations.html
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Expand Up @@ -1180,9 +1180,9 @@ <h2 data-number="11.9" class="anchored" data-anchor-id="bonus-calculating-consta
<p>Earlier, we calculated the constant model MSE using calculus. It turns out that there is a much more elegant way of performing this same minimization algebraically, without using calculus at all.</p>
<p>In this calculation, we use the fact that the <strong>sum of deviations from the mean is 0</strong> or that <span class="math inline">\(\sum_{i=1}^{n} (y_i - \bar{y}) = 0\)</span>.</p>
<p>Let’s quickly walk through the proof for this: <span class="math display">\[\sum_{i=1}^{n} (y_i - \bar{y}) = \sum_{i=1}^{n} y_i - \sum_{i=1}^{n} \bar{y}\]</span></p>
<p><span class="math display">\[ = \sum\_{i=1}^{n} y_i - n\bar{y}\]</span></p>
<p><span class="math display">\[ = \sum*{i=1}^{n} y_i - n\frac{1}{n}\sum*{i=1}^{n}y\]</span></p>
<p><span class="math display">\[ = \sum*{i=1}^{n} y_i - \sum*{i=1}^{n}y_i\]</span></p>
<p><span class="math display">\[ = \sum_{i=1}^{n} y_i - n\bar{y}\]</span></p>
<p><span class="math display">\[ = \sum_{i=1}^{n} y_i - n\frac{1}{n}\sum_{i=1}^{n}y\]</span></p>
<p><span class="math display">\[ = \sum_{i=1}^{n} y_i - \sum_{i=1}^{n}y_i\]</span></p>
<p>In our calculations, we’ll also be using the definition of the variance as a sample. As a refresher:</p>
<p><span class="math display">\[\sigma_y^2 = \frac{1}{n}\sum_{i=1}^{n} (y_i - \bar{y})^2\]</span></p>
<p>Getting into our calculation for MSE minimization:</p>
Expand Down Expand Up @@ -2333,11 +2333,11 @@ <h5 data-number="11.9.0.0.1" class="anchored" data-anchor-id="note"><span class=
<span id="cb29-860"><a href="#cb29-860" aria-hidden="true" tabindex="-1"></a>Let's quickly walk through the proof for this:</span>
<span id="cb29-861"><a href="#cb29-861" aria-hidden="true" tabindex="-1"></a>$$\sum_{i=1}^{n} (y_i - \bar{y}) = \sum_{i=1}^{n} y_i - \sum_{i=1}^{n} \bar{y}$$</span>
<span id="cb29-862"><a href="#cb29-862" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb29-863"><a href="#cb29-863" aria-hidden="true" tabindex="-1"></a>$$ = \sum<span class="sc">\_</span>{i=1}^{n} y_i - n\bar{y}$$</span>
<span id="cb29-863"><a href="#cb29-863" aria-hidden="true" tabindex="-1"></a>$$ = \sum_{i=1}^{n} y_i - n\bar{y}$$</span>
<span id="cb29-864"><a href="#cb29-864" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb29-865"><a href="#cb29-865" aria-hidden="true" tabindex="-1"></a>$$ = \sum*{i=1}^{n} y_i - n\frac{1}{n}\sum*{i=1}^{n}y$$</span>
<span id="cb29-865"><a href="#cb29-865" aria-hidden="true" tabindex="-1"></a>$$ = \sum_{i=1}^{n} y_i - n\frac{1}{n}\sum_{i=1}^{n}y$$</span>
<span id="cb29-866"><a href="#cb29-866" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb29-867"><a href="#cb29-867" aria-hidden="true" tabindex="-1"></a>$$ = \sum*{i=1}^{n} y_i - \sum*{i=1}^{n}y_i$$</span>
<span id="cb29-867"><a href="#cb29-867" aria-hidden="true" tabindex="-1"></a>$$ = \sum_{i=1}^{n} y_i - \sum_{i=1}^{n}y_i$$</span>
<span id="cb29-868"><a href="#cb29-868" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb29-869"><a href="#cb29-869" aria-hidden="true" tabindex="-1"></a>In our calculations, we'll also be using the definition of the variance as a sample. As a refresher:</span>
<span id="cb29-870"><a href="#cb29-870" aria-hidden="true" tabindex="-1"></a></span>
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70 changes: 35 additions & 35 deletions docs/pandas_2/pandas_2.html
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Expand Up @@ -1602,12 +1602,12 @@ <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">328525</td>
<td data-quarto-table-cell-role="th">384635</td>
<td>CA</td>
<td>M</td>
<td>1994</td>
<td>Refugio</td>
<td>17</td>
<td>2015</td>
<td>August</td>
<td>177</td>
</tr>
</tbody>
</table>
Expand All @@ -1634,34 +1634,34 @@ <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">337557</td>
<td>1998</td>
<td>Ryan</td>
<td>2432</td>
<td data-quarto-table-cell-role="th">229975</td>
<td>2020</td>
<td>Alyana</td>
<td>17</td>
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<td data-quarto-table-cell-role="th">353111</td>
<td>2004</td>
<td>Rylan</td>
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<td>1964</td>
<td>Joanie</td>
<td>9</td>
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<td data-quarto-table-cell-role="th">274384</td>
<td>1962</td>
<td>Gerhard</td>
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<td>1995</td>
<td>Antonino</td>
<td>5</td>
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<td data-quarto-table-cell-role="th">251406</td>
<td>1935</td>
<td>Lester</td>
<td>41</td>
<td data-quarto-table-cell-role="th">89092</td>
<td>1982</td>
<td>Doris</td>
<td>44</td>
</tr>
<tr class="odd">
<td data-quarto-table-cell-role="th">48869</td>
<td>1963</td>
<td>Terilyn</td>
<td>8</td>
<td data-quarto-table-cell-role="th">7620</td>
<td>1925</td>
<td>Hiroko</td>
<td>6</td>
</tr>
</tbody>
</table>
Expand All @@ -1687,27 +1687,27 @@ <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">343302</td>
<td data-quarto-table-cell-role="th">149281</td>
<td>2000</td>
<td>Timmy</td>
<td>21</td>
<td>Jada</td>
<td>193</td>
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<td data-quarto-table-cell-role="th">151635</td>
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<td>2000</td>
<td>Victor</td>
<td>8</td>
<td>Israel</td>
<td>374</td>
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<td data-quarto-table-cell-role="th">150822</td>
<td data-quarto-table-cell-role="th">344601</td>
<td>2000</td>
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<td>Zayd</td>
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<td data-quarto-table-cell-role="th">152044</td>
<td data-quarto-table-cell-role="th">152062</td>
<td>2000</td>
<td>Hania</td>
<td>Jaileen</td>
<td>6</td>
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</tbody>
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14 changes: 7 additions & 7 deletions docs/pandas_3/pandas_3.html
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4 changes: 2 additions & 2 deletions docs/regex/regex.html
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Expand Up @@ -638,11 +638,11 @@ <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_6509/2523629438.py:3: FutureWarning:
<pre><code>/var/folders/7t/zbwy02ts2m7cn64fvwjqb8xw0000gp/T/ipykernel_68270/2523629438.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_6509/2523629438.py:3: FutureWarning:
/var/folders/7t/zbwy02ts2m7cn64fvwjqb8xw0000gp/T/ipykernel_68270/2523629438.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>
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6 changes: 3 additions & 3 deletions docs/sampling/sampling.html
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Expand Up @@ -656,7 +656,7 @@ <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>0.5304983917461519</code></pre>
<pre><code>0.5293715010740242</code></pre>
</div>
</div>
<p>This is very close to the actual vote of 0.5302792307692308!</p>
Expand All @@ -674,7 +674,7 @@ <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> = 0.5275, <strong>Err</strong> = 0.52%.</p>
<p><strong>Actual</strong> = 0.5303, <strong>Sample</strong> = 0.5325, <strong>Err</strong> = 0.42%.</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>
Expand Down Expand Up @@ -707,7 +707,7 @@ <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>0.944</code></pre>
<pre><code>0.952</code></pre>
</div>
</div>
<p>You can see the curve looks roughly Gaussian/normal. Using KDE:</p>
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471 changes: 0 additions & 471 deletions docs/search.json
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14 changes: 7 additions & 7 deletions index.log
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