last version for lecture

2025-09-07 22:08:05 +02:00
parent 151ee978c0
commit 999b7d51aa
7 changed files with 184 additions and 184 deletions
@@ -359,7 +359,7 @@ X \equiv \begin{bmatrix}
 \end{bmatrix}.
 $$

-<p>The cost/loss/risk function is given by (</p>
+<p>The cost/loss/risk function is given by </p>
 $$
 C(\theta) = \frac{1}{n}||X\theta-\mathbf{y}||_{2}^{2} = \frac{1}{n}\sum_{i=1}^{100}\left[ (\theta_0 + \theta_1 x_i)^2 - 2 y_i (\theta_0 + \theta_1 x_i) + y_i^2\right] 
 $$
@@ -304,7 +304,7 @@ X \equiv \begin{bmatrix}
 $$
 <p>&nbsp;<br>

-<p>The cost/loss/risk function is given by (</p>
+<p>The cost/loss/risk function is given by </p>
 <p>&nbsp;<br>
 $$
 C(\theta) = \frac{1}{n}||X\theta-\mathbf{y}||_{2}^{2} = \frac{1}{n}\sum_{i=1}^{100}\left[ (\theta_0 + \theta_1 x_i)^2 - 2 y_i (\theta_0 + \theta_1 x_i) + y_i^2\right] 
@@ -405,7 +405,7 @@ X \equiv \begin{bmatrix}
 \end{bmatrix}.
 $$

-<p>The cost/loss/risk function is given by (</p>
+<p>The cost/loss/risk function is given by </p>
 $$
 C(\theta) = \frac{1}{n}||X\theta-\mathbf{y}||_{2}^{2} = \frac{1}{n}\sum_{i=1}^{100}\left[ (\theta_0 + \theta_1 x_i)^2 - 2 y_i (\theta_0 + \theta_1 x_i) + y_i^2\right] 
 $$
@@ -482,7 +482,7 @@ X \equiv \begin{bmatrix}
 \end{bmatrix}.
 $$

-<p>The cost/loss/risk function is given by (</p>
+<p>The cost/loss/risk function is given by </p>
 $$
 C(\theta) = \frac{1}{n}||X\theta-\mathbf{y}||_{2}^{2} = \frac{1}{n}\sum_{i=1}^{100}\left[ (\theta_0 + \theta_1 x_i)^2 - 2 y_i (\theta_0 + \theta_1 x_i) + y_i^2\right] 
 $$
@@ -84,7 +84,7 @@ X \equiv \begin{bmatrix}
 \end{bmatrix}.
 \]
 !et
-The cost/loss/risk function is given by (
+The cost/loss/risk function is given by 
 !bt
 \[
 C(\theta) = \frac{1}{n}||X\theta-\mathbf{y}||_{2}^{2} = \frac{1}{n}\sum_{i=1}^{100}\left[ (\theta_0 + \theta_1 x_i)^2 - 2 y_i (\theta_0 + \theta_1 x_i) + y_i^2\right]