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>

doc/pub/week36/ipynb/week36.ipynb

@@ -970,7 +970,7 @@
     "## Lasso case\n",
     "\n",
     "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 $\\beta_0$\n",
-    "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"
    ]
   },
   {
@@ -1511,7 +1511,7 @@
    "metadata": {},
    "source": [
     "$$\n",
-    "\\hat{\\boldsymbol{\\beta}}_{mathrm{OLS}}=\\left(\\boldsymbol{X}^T\\boldsymbol{X}\\right^{-1}\\boldsymbol{X}^T\\boldsymbol{y}!\n",
+    "\\hat{\\boldsymbol{\\beta}}_{\\mathrm{OLS}}=\\left(\\boldsymbol{X}^T\\boldsymbol{X}\\right)^{-1}\\boldsymbol{X}^T\\boldsymbol{y}!\n",
     "$$"
    ]
   },

doc/src/week36/week36.do.txt

@@ -531,7 +531,7 @@ which gives $\lambda=4.571$ and $\beta_0=0.933$ and $\beta_1=0.359$.
 ===== Lasso case =====
 
 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
 !bt
 \[
 C(\bm{\beta})=(4-2\beta_0)^2+(2-\beta_1)^2+\lambda(\vert\beta_0\vert+\vert\beta_1\vert),
@@ -856,7 +856,7 @@ Taking the derivative of the *new* cost function with respect to the parameters
 which leads to
 !bt
 \[
-\hat{\bm{\beta}}_{mathrm{OLS}}=\left(\bm{X}^T\bm{X}\right^{-1}\bm{X}^T\bm{y}!
+\hat{\bm{\beta}}_{\mathrm{OLS}}=\left(\bm{X}^T\bm{X}\right)^{-1}\bm{X}^T\bm{y}!
 \]
 !et