update

doc/pub/week36/html/week36-reveal.html

@@ -787,7 +787,7 @@ which gives \( \lambda=4.571 \) and \( \beta_0=0.933 \) and \( \beta_1=0.359 \).
 
 <p>
 For Lasso we need now, keeping a  constraint on \( \vert\beta_0\vert+\vert\beta_1\vert=1 \),  to take the derivative of the absolute values of \( \beta_0 \)
-and \( beta_1 \). This gives us the following derivatives of the cost function
+and \( \beta_1 \). This gives us the following derivatives of the cost function
 <p>&nbsp;<br>
 $$
 C(\boldsymbol{\beta})=(4-2\beta_0)^2+(2-\beta_1)^2+\lambda(\vert\beta_0\vert+\vert\beta_1\vert),
@@ -1176,7 +1176,7 @@ $$
 which leads to
 <p>&nbsp;<br>
 $$
-\hat{\boldsymbol{\beta}}_{mathrm{OLS}}=\left(\boldsymbol{X}^T\boldsymbol{X}\right^{-1}\boldsymbol{X}^T\boldsymbol{y}!
+\hat{\boldsymbol{\beta}}_{\mathrm{OLS}}=\left(\boldsymbol{X}^T\boldsymbol{X}\right)^{-1}\boldsymbol{X}^T\boldsymbol{y}!
 $$
 <p>&nbsp;<br>
 </section>

doc/pub/week36/html/week36-solarized.html

@@ -808,7 +808,7 @@ which gives \( \lambda=4.571 \) and \( \beta_0=0.933 \) and \( \beta_1=0.359 \).
 
 <p>
 For Lasso we need now, keeping a  constraint on \( \vert\beta_0\vert+\vert\beta_1\vert=1 \),  to take the derivative of the absolute values of \( \beta_0 \)
-and \( beta_1 \). This gives us the following derivatives of the cost function
+and \( \beta_1 \). This gives us the following derivatives of the cost function
 $$
 C(\boldsymbol{\beta})=(4-2\beta_0)^2+(2-\beta_1)^2+\lambda(\vert\beta_0\vert+\vert\beta_1\vert),
 $$
@@ -1150,7 +1150,7 @@ $$
 
 which leads to
 $$
-\hat{\boldsymbol{\beta}}_{mathrm{OLS}}=\left(\boldsymbol{X}^T\boldsymbol{X}\right^{-1}\boldsymbol{X}^T\boldsymbol{y}!
+\hat{\boldsymbol{\beta}}_{\mathrm{OLS}}=\left(\boldsymbol{X}^T\boldsymbol{X}\right)^{-1}\boldsymbol{X}^T\boldsymbol{y}!
 $$
 
 <p>

doc/pub/week36/html/week36.html

@@ -813,7 +813,7 @@ which gives \( \lambda=4.571 \) and \( \beta_0=0.933 \) and \( \beta_1=0.359 \).
 
 <p>
 For Lasso we need now, keeping a  constraint on \( \vert\beta_0\vert+\vert\beta_1\vert=1 \),  to take the derivative of the absolute values of \( \beta_0 \)
-and \( beta_1 \). This gives us the following derivatives of the cost function
+and \( \beta_1 \). This gives us the following derivatives of the cost function
 $$
 C(\boldsymbol{\beta})=(4-2\beta_0)^2+(2-\beta_1)^2+\lambda(\vert\beta_0\vert+\vert\beta_1\vert),
 $$
@@ -1155,7 +1155,7 @@ $$
 
 which leads to
 $$
-\hat{\boldsymbol{\beta}}_{mathrm{OLS}}=\left(\boldsymbol{X}^T\boldsymbol{X}\right^{-1}\boldsymbol{X}^T\boldsymbol{y}!
+\hat{\boldsymbol{\beta}}_{\mathrm{OLS}}=\left(\boldsymbol{X}^T\boldsymbol{X}\right)^{-1}\boldsymbol{X}^T\boldsymbol{y}!
 $$
 
 <p>