typo

doc/pub/week37/html/._week37-bs006.html

@@ -271,12 +271,12 @@ MathJax.Hub.Config({
 <p>We could now define a new cost function to minimize, namely the negative logarithm of the above PDF</p>
 
 $$
-C(\boldsymbol{\beta}=-\log{\prod_{i=0}^{n-1}p(y_i,\boldsymbol{X}\vert\boldsymbol{\beta})}=-\sum_{i=0}^{n-1}\log{p(y_i,\boldsymbol{X}\vert\boldsymbol{\beta})},
+C(\boldsymbol{\beta})=-\log{\prod_{i=0}^{n-1}p(y_i,\boldsymbol{X}\vert\boldsymbol{\beta})}=-\sum_{i=0}^{n-1}\log{p(y_i,\boldsymbol{X}\vert\boldsymbol{\beta})},
 $$
 
 <p>which becomes</p>
 $$
-C(\boldsymbol{\beta}=\frac{n}{2}\log{2\pi\sigma^2}+\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta})\vert\vert_2^2}{2\sigma^2}.
+C(\boldsymbol{\beta})=\frac{n}{2}\log{2\pi\sigma^2}+\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta})\vert\vert_2^2}{2\sigma^2}.
 $$
 
 <p>Taking the derivative of the <em>new</em> cost function with respect to the parameters \( \beta \) we recognize our familiar OLS equation, namely</p>

doc/pub/week37/html/week37-reveal.html

@@ -319,14 +319,14 @@ is equivalent to the maximization/minimization of the function itself.
 
 <p>&nbsp;<br>
 $$
-C(\boldsymbol{\beta}=-\log{\prod_{i=0}^{n-1}p(y_i,\boldsymbol{X}\vert\boldsymbol{\beta})}=-\sum_{i=0}^{n-1}\log{p(y_i,\boldsymbol{X}\vert\boldsymbol{\beta})},
+C(\boldsymbol{\beta})=-\log{\prod_{i=0}^{n-1}p(y_i,\boldsymbol{X}\vert\boldsymbol{\beta})}=-\sum_{i=0}^{n-1}\log{p(y_i,\boldsymbol{X}\vert\boldsymbol{\beta})},
 $$
 <p>&nbsp;<br>
 
 <p>which becomes</p>
 <p>&nbsp;<br>
 $$
-C(\boldsymbol{\beta}=\frac{n}{2}\log{2\pi\sigma^2}+\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta})\vert\vert_2^2}{2\sigma^2}.
+C(\boldsymbol{\beta})=\frac{n}{2}\log{2\pi\sigma^2}+\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta})\vert\vert_2^2}{2\sigma^2}.
 $$
 <p>&nbsp;<br>
 

doc/pub/week37/html/week37-solarized.html

@@ -349,12 +349,12 @@ is equivalent to the maximization/minimization of the function itself.
 <p>We could now define a new cost function to minimize, namely the negative logarithm of the above PDF</p>
 
 $$
-C(\boldsymbol{\beta}=-\log{\prod_{i=0}^{n-1}p(y_i,\boldsymbol{X}\vert\boldsymbol{\beta})}=-\sum_{i=0}^{n-1}\log{p(y_i,\boldsymbol{X}\vert\boldsymbol{\beta})},
+C(\boldsymbol{\beta})=-\log{\prod_{i=0}^{n-1}p(y_i,\boldsymbol{X}\vert\boldsymbol{\beta})}=-\sum_{i=0}^{n-1}\log{p(y_i,\boldsymbol{X}\vert\boldsymbol{\beta})},
 $$
 
 <p>which becomes</p>
 $$
-C(\boldsymbol{\beta}=\frac{n}{2}\log{2\pi\sigma^2}+\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta})\vert\vert_2^2}{2\sigma^2}.
+C(\boldsymbol{\beta})=\frac{n}{2}\log{2\pi\sigma^2}+\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta})\vert\vert_2^2}{2\sigma^2}.
 $$
 
 <p>Taking the derivative of the <em>new</em> cost function with respect to the parameters \( \beta \) we recognize our familiar OLS equation, namely</p>

doc/pub/week37/html/week37.html

@@ -426,12 +426,12 @@ is equivalent to the maximization/minimization of the function itself.
 <p>We could now define a new cost function to minimize, namely the negative logarithm of the above PDF</p>
 
 $$
-C(\boldsymbol{\beta}=-\log{\prod_{i=0}^{n-1}p(y_i,\boldsymbol{X}\vert\boldsymbol{\beta})}=-\sum_{i=0}^{n-1}\log{p(y_i,\boldsymbol{X}\vert\boldsymbol{\beta})},
+C(\boldsymbol{\beta})=-\log{\prod_{i=0}^{n-1}p(y_i,\boldsymbol{X}\vert\boldsymbol{\beta})}=-\sum_{i=0}^{n-1}\log{p(y_i,\boldsymbol{X}\vert\boldsymbol{\beta})},
 $$
 
 <p>which becomes</p>
 $$
-C(\boldsymbol{\beta}=\frac{n}{2}\log{2\pi\sigma^2}+\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta})\vert\vert_2^2}{2\sigma^2}.
+C(\boldsymbol{\beta})=\frac{n}{2}\log{2\pi\sigma^2}+\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta})\vert\vert_2^2}{2\sigma^2}.
 $$
 
 <p>Taking the derivative of the <em>new</em> cost function with respect to the parameters \( \beta \) we recognize our familiar OLS equation, namely</p>

doc/src/week37/week37.do.txt

@@ -113,13 +113,13 @@ We could now define a new cost function to minimize, namely the negative logarit
 
 !bt
 \[
-C(\bm{\beta}=-\log{\prod_{i=0}^{n-1}p(y_i,\bm{X}\vert\bm{\beta})}=-\sum_{i=0}^{n-1}\log{p(y_i,\bm{X}\vert\bm{\beta})},
+C(\bm{\beta})=-\log{\prod_{i=0}^{n-1}p(y_i,\bm{X}\vert\bm{\beta})}=-\sum_{i=0}^{n-1}\log{p(y_i,\bm{X}\vert\bm{\beta})},
 \]
 !et
 which becomes
 !bt
 \[
-C(\bm{\beta}=\frac{n}{2}\log{2\pi\sigma^2}+\frac{\vert\vert (\bm{y}-\bm{X}\bm{\beta})\vert\vert_2^2}{2\sigma^2}.
+C(\bm{\beta})=\frac{n}{2}\log{2\pi\sigma^2}+\frac{\vert\vert (\bm{y}-\bm{X}\bm{\beta})\vert\vert_2^2}{2\sigma^2}.
 \]
 !et