fix typo in OLS summary table

DS-100 · Feb 27, 2024 · 2c00cdc · 2c00cdc
1 parent edda08b
commit 2c00cdc
Show file tree

Hide file tree

Showing 41 changed files with 145 additions and 616 deletions.
diff --git a/...oss_transformations/loss_transformations_files/figure-html/cell-17-output-1.png b/...oss_transformations/loss_transformations_files/figure-html/cell-17-output-1.png
diff --git a/...oss_transformations/loss_transformations_files/figure-html/cell-18-output-1.png b/...oss_transformations/loss_transformations_files/figure-html/cell-18-output-1.png
diff --git a/...oss_transformations/loss_transformations_files/figure-html/cell-20-output-1.png b/...oss_transformations/loss_transformations_files/figure-html/cell-20-output-1.png
diff --git a/...loss_transformations/loss_transformations_files/figure-html/cell-4-output-1.png b/...loss_transformations/loss_transformations_files/figure-html/cell-4-output-1.png
diff --git a/...loss_transformations/loss_transformations_files/figure-html/cell-6-output-1.png b/...loss_transformations/loss_transformations_files/figure-html/cell-6-output-1.png
diff --git a/...loss_transformations/loss_transformations_files/figure-html/cell-8-output-1.png b/...loss_transformations/loss_transformations_files/figure-html/cell-8-output-1.png
diff --git a/docs/ols/ols.html b/docs/ols/ols.html
@@ -994,7 +994,7 @@ <h2 data-number="12.4" class="anchored" data-anchor-id="ols-properties"><span cl
 <tr class="odd">
 <td>Simple Linear Regression + MSE</td>
 <td><span class="math inline">\(\hat{y} = \theta_0 + \theta_1x\)</span></td>
-<td><span class="math inline">\(\hat{\theta}_0 = \bar{y} - \hat{\theta}_1\hat{x}\)</span> <span class="math inline">\(\hat{\theta}_1 = r\frac{\sigma_y}{\sigma_x}\)</span></td>
+<td><span class="math inline">\(\hat{\theta}_0 = \bar{y} - \hat{\theta}_1\bar{x}\)</span> <span class="math inline">\(\hat{\theta}_1 = r\frac{\sigma_y}{\sigma_x}\)</span></td>
 <td><strong>Yes</strong>. Any set of non-constant* values has a unique mean, SD, and correlation coefficient.</td>
 </tr>
 <tr class="even">
@@ -1824,7 +1824,7 @@ <h2 data-number="12.5" class="anchored" data-anchor-id="bonus-uniqueness-of-the-
 <span id="cb4-480"><a href="#cb4-480" aria-hidden="true" tabindex="-1"></a>| -- | -- | -- |  -- | </span>
 <span id="cb4-481"><a href="#cb4-481" aria-hidden="true" tabindex="-1"></a>| Constant Model + MSE | $\hat{y} = \theta_0$| $\hat{\theta}_0 = mean(y) = \bar{y}$ | **Yes**. Any set of values has a unique mean.</span>
 <span id="cb4-482"><a href="#cb4-482" aria-hidden="true" tabindex="-1"></a>| Constant Model + MAE | $\hat{y} = \theta_0$  | $\hat{\theta}_0 = median(y)$ | **Yes**, if odd. **No**, if even. Return the average of the middle 2 values.</span>
-<span id="cb4-483"><a href="#cb4-483" aria-hidden="true" tabindex="-1"></a>| Simple Linear Regression + MSE | $\hat{y} = \theta_0 + \theta_1x$| $\hat{\theta}_0 = \bar{y} - \hat{\theta}_1\hat{x}$ $\hat{\theta}_1 = r\frac{\sigma_y}{\sigma_x}$| **Yes**. Any set of non-constant* values has a unique mean, SD, and correlation coefficient.</span>
+<span id="cb4-483"><a href="#cb4-483" aria-hidden="true" tabindex="-1"></a>| Simple Linear Regression + MSE | $\hat{y} = \theta_0 + \theta_1x$| $\hat{\theta}_0 = \bar{y} - \hat{\theta}_1\bar{x}$ $\hat{\theta}_1 = r\frac{\sigma_y}{\sigma_x}$| **Yes**. Any set of non-constant* values has a unique mean, SD, and correlation coefficient.</span>
 <span id="cb4-484"><a href="#cb4-484" aria-hidden="true" tabindex="-1"></a>| **OLS** (Linear Model + MSE) | $\mathbb{\hat{Y}} = \mathbb{X}\mathbb{\theta}$| $\hat{\theta} = (\mathbb{X}^T\mathbb{X})^{-1}\mathbb{X}^T\mathbb{Y}$  | **Yes**, if $\mathbb{X}$ is full column rank (all columns are linearly independent, # of datapoints &gt;&gt;&gt; # of features).</span>
 <span id="cb4-485"><a href="#cb4-485" aria-hidden="true" tabindex="-1"></a></span>
 <span id="cb4-486"><a href="#cb4-486" aria-hidden="true" tabindex="-1"></a><span class="fu">## Bonus: Uniqueness of the Solution</span></span>

diff --git a/docs/sampling/sampling_files/figure-html/cell-11-output-2.png b/docs/sampling/sampling_files/figure-html/cell-11-output-2.png
diff --git a/docs/sampling/sampling_files/figure-html/cell-22-output-2.png b/docs/sampling/sampling_files/figure-html/cell-22-output-2.png
diff --git a/docs/sampling/sampling_files/figure-html/cell-25-output-2.png b/docs/sampling/sampling_files/figure-html/cell-25-output-2.png
diff --git a/docs/sampling/sampling_files/figure-html/cell-8-output-2.png b/docs/sampling/sampling_files/figure-html/cell-8-output-2.png
diff --git a/docs/search.json b/docs/search.json
diff --git a/docs/visualization_1/visualization_1_files/figure-html/cell-25-output-1.png b/docs/visualization_1/visualization_1_files/figure-html/cell-25-output-1.png
diff --git a/docs/visualization_1/visualization_1_files/figure-html/cell-26-output-1.png b/docs/visualization_1/visualization_1_files/figure-html/cell-26-output-1.png
diff --git a/docs/visualization_1/visualization_1_files/figure-html/cell-27-output-1.png b/docs/visualization_1/visualization_1_files/figure-html/cell-27-output-1.png
diff --git a/docs/visualization_1/visualization_1_files/figure-html/cell-28-output-1.png b/docs/visualization_1/visualization_1_files/figure-html/cell-28-output-1.png
diff --git a/docs/visualization_1/visualization_1_files/figure-html/cell-29-output-1.png b/docs/visualization_1/visualization_1_files/figure-html/cell-29-output-1.png
diff --git a/docs/visualization_1/visualization_1_files/figure-html/cell-30-output-1.png b/docs/visualization_1/visualization_1_files/figure-html/cell-30-output-1.png
diff --git a/docs/visualization_1/visualization_1_files/figure-html/cell-31-output-1.png b/docs/visualization_1/visualization_1_files/figure-html/cell-31-output-1.png
diff --git a/docs/visualization_1/visualization_1_files/figure-html/cell-32-output-1.png b/docs/visualization_1/visualization_1_files/figure-html/cell-32-output-1.png
diff --git a/docs/visualization_2/visualization_2_files/figure-html/cell-10-output-2.png b/docs/visualization_2/visualization_2_files/figure-html/cell-10-output-2.png
diff --git a/docs/visualization_2/visualization_2_files/figure-html/cell-13-output-2.png b/docs/visualization_2/visualization_2_files/figure-html/cell-13-output-2.png
diff --git a/docs/visualization_2/visualization_2_files/figure-html/cell-18-output-2.png b/docs/visualization_2/visualization_2_files/figure-html/cell-18-output-2.png
diff --git a/docs/visualization_2/visualization_2_files/figure-html/cell-19-output-2.png b/docs/visualization_2/visualization_2_files/figure-html/cell-19-output-2.png
diff --git a/docs/visualization_2/visualization_2_files/figure-html/cell-20-output-2.png b/docs/visualization_2/visualization_2_files/figure-html/cell-20-output-2.png
diff --git a/docs/visualization_2/visualization_2_files/figure-html/cell-20-output-3.png b/docs/visualization_2/visualization_2_files/figure-html/cell-20-output-3.png
diff --git a/docs/visualization_2/visualization_2_files/figure-html/cell-24-output-1.png b/docs/visualization_2/visualization_2_files/figure-html/cell-24-output-1.png
diff --git a/docs/visualization_2/visualization_2_files/figure-html/cell-26-output-1.png b/docs/visualization_2/visualization_2_files/figure-html/cell-26-output-1.png
diff --git a/docs/visualization_2/visualization_2_files/figure-html/cell-27-output-1.png b/docs/visualization_2/visualization_2_files/figure-html/cell-27-output-1.png
diff --git a/docs/visualization_2/visualization_2_files/figure-html/cell-28-output-1.png b/docs/visualization_2/visualization_2_files/figure-html/cell-28-output-1.png
diff --git a/docs/visualization_2/visualization_2_files/figure-html/cell-29-output-1.png b/docs/visualization_2/visualization_2_files/figure-html/cell-29-output-1.png
diff --git a/docs/visualization_2/visualization_2_files/figure-html/cell-30-output-1.png b/docs/visualization_2/visualization_2_files/figure-html/cell-30-output-1.png
diff --git a/docs/visualization_2/visualization_2_files/figure-html/cell-31-output-1.png b/docs/visualization_2/visualization_2_files/figure-html/cell-31-output-1.png
diff --git a/docs/visualization_2/visualization_2_files/figure-html/cell-31-output-2.png b/docs/visualization_2/visualization_2_files/figure-html/cell-31-output-2.png
diff --git a/docs/visualization_2/visualization_2_files/figure-html/cell-32-output-1.png b/docs/visualization_2/visualization_2_files/figure-html/cell-32-output-1.png
diff --git a/docs/visualization_2/visualization_2_files/figure-html/cell-32-output-2.png b/docs/visualization_2/visualization_2_files/figure-html/cell-32-output-2.png
diff --git a/docs/visualization_2/visualization_2_files/figure-html/cell-33-output-1.png b/docs/visualization_2/visualization_2_files/figure-html/cell-33-output-1.png
diff --git a/index.log b/index.log
diff --git a/index.pdf b/index.pdf
diff --git a/index.tex b/index.tex
diff --git a/ols/ols.qmd b/ols/ols.qmd
@@ -474,7 +474,7 @@ To summarize:
 | -- | -- | -- |  -- | 
 | Constant Model + MSE | $\hat{y} = \theta_0$| $\hat{\theta}_0 = mean(y) = \bar{y}$ | **Yes**. Any set of values has a unique mean.
 | Constant Model + MAE | $\hat{y} = \theta_0$  | $\hat{\theta}_0 = median(y)$ | **Yes**, if odd. **No**, if even. Return the average of the middle 2 values.
-| Simple Linear Regression + MSE | $\hat{y} = \theta_0 + \theta_1x$| $\hat{\theta}_0 = \bar{y} - \hat{\theta}_1\hat{x}$ $\hat{\theta}_1 = r\frac{\sigma_y}{\sigma_x}$| **Yes**. Any set of non-constant* values has a unique mean, SD, and correlation coefficient.
+| Simple Linear Regression + MSE | $\hat{y} = \theta_0 + \theta_1x$| $\hat{\theta}_0 = \bar{y} - \hat{\theta}_1\bar{x}$ $\hat{\theta}_1 = r\frac{\sigma_y}{\sigma_x}$| **Yes**. Any set of non-constant* values has a unique mean, SD, and correlation coefficient.
 | **OLS** (Linear Model + MSE) | $\mathbb{\hat{Y}} = \mathbb{X}\mathbb{\theta}$| $\hat{\theta} = (\mathbb{X}^T\mathbb{X})^{-1}\mathbb{X}^T\mathbb{Y}$  | **Yes**, if $\mathbb{X}$ is full column rank (all columns are linearly independent, # of datapoints >>> # of features).
 
 ## Bonus: Uniqueness of the Solution