typos

doc/pub/week35/html/._week35-bs067.html

@@ -298,7 +298,7 @@ $$
 
 <p>In this case the standard OLS results in </p>
 $$
-\boldsymbol{\beta}^{\mathrm{OLS}} = \boldsymbol{X}^T\boldsymbol{y}=\sum_{i=0}^{p-1}\boldsymbol{u}_j\boldsymbol{u}_j^T\boldsymbol{y},
+\boldsymbol{\beta}^{\mathrm{OLS}} = \boldsymbol{X}^T\boldsymbol{y}=\sum_{i=0}^{n-1}\boldsymbol{u}_i\boldsymbol{u}_i^T\boldsymbol{y},
 $$
 
 <p>and</p>

doc/pub/week35/html/._week35-bs068.html

@@ -309,7 +309,7 @@ $$
 
 <p>and reordering we have</p>
 $$
-\boldsymbol{X}^T\boldsymbol{X}\boldsymbol{\beta})+\lambda sgn(\boldsymbol{\beta})=2\boldsymbol{X}^T(\boldsymbol{y}.
+\boldsymbol{X}^T\boldsymbol{X}\boldsymbol{\beta}+\lambda sgn(\boldsymbol{\beta})=2\boldsymbol{X}^T\boldsymbol{y}.
 $$
 
 <p>This equation does not lead to a nice analytical equation as in either Ridge regression or ordinary least squares. This equation can however be solved by using standard convex optimization algorithms using for example the Python package <a href="https://cvxopt.org/" target="_self">CVXOPT</a>. We will discuss this later. </p>

doc/pub/week35/html/week35-reveal.html

@@ -3422,7 +3422,7 @@ $$
 <p>In this case the standard OLS results in </p>
 <p>&nbsp;<br>
 $$
-\boldsymbol{\beta}^{\mathrm{OLS}} = \boldsymbol{X}^T\boldsymbol{y}=\sum_{i=0}^{p-1}\boldsymbol{u}_j\boldsymbol{u}_j^T\boldsymbol{y},
+\boldsymbol{\beta}^{\mathrm{OLS}} = \boldsymbol{X}^T\boldsymbol{y}=\sum_{i=0}^{n-1}\boldsymbol{u}_i\boldsymbol{u}_i^T\boldsymbol{y},
 $$
 <p>&nbsp;<br>
 
@@ -3475,7 +3475,7 @@ $$
 <p>and reordering we have</p>
 <p>&nbsp;<br>
 $$
-\boldsymbol{X}^T\boldsymbol{X}\boldsymbol{\beta})+\lambda sgn(\boldsymbol{\beta})=2\boldsymbol{X}^T(\boldsymbol{y}.
+\boldsymbol{X}^T\boldsymbol{X}\boldsymbol{\beta}+\lambda sgn(\boldsymbol{\beta})=2\boldsymbol{X}^T\boldsymbol{y}.
 $$
 <p>&nbsp;<br>
 

doc/pub/week35/html/week35-solarized.html

@@ -3273,7 +3273,7 @@ $$
 
 <p>In this case the standard OLS results in </p>
 $$
-\boldsymbol{\beta}^{\mathrm{OLS}} = \boldsymbol{X}^T\boldsymbol{y}=\sum_{i=0}^{p-1}\boldsymbol{u}_j\boldsymbol{u}_j^T\boldsymbol{y},
+\boldsymbol{\beta}^{\mathrm{OLS}} = \boldsymbol{X}^T\boldsymbol{y}=\sum_{i=0}^{n-1}\boldsymbol{u}_i\boldsymbol{u}_i^T\boldsymbol{y},
 $$
 
 <p>and</p>
@@ -3315,7 +3315,7 @@ $$
 
 <p>and reordering we have</p>
 $$
-\boldsymbol{X}^T\boldsymbol{X}\boldsymbol{\beta})+\lambda sgn(\boldsymbol{\beta})=2\boldsymbol{X}^T(\boldsymbol{y}.
+\boldsymbol{X}^T\boldsymbol{X}\boldsymbol{\beta}+\lambda sgn(\boldsymbol{\beta})=2\boldsymbol{X}^T\boldsymbol{y}.
 $$
 
 <p>This equation does not lead to a nice analytical equation as in either Ridge regression or ordinary least squares. This equation can however be solved by using standard convex optimization algorithms using for example the Python package <a href="https://cvxopt.org/" target="_blank">CVXOPT</a>. We will discuss this later. </p>

doc/pub/week35/html/week35.html

@@ -3350,7 +3350,7 @@ $$
 
 <p>In this case the standard OLS results in </p>
 $$
-\boldsymbol{\beta}^{\mathrm{OLS}} = \boldsymbol{X}^T\boldsymbol{y}=\sum_{i=0}^{p-1}\boldsymbol{u}_j\boldsymbol{u}_j^T\boldsymbol{y},
+\boldsymbol{\beta}^{\mathrm{OLS}} = \boldsymbol{X}^T\boldsymbol{y}=\sum_{i=0}^{n-1}\boldsymbol{u}_i\boldsymbol{u}_i^T\boldsymbol{y},
 $$
 
 <p>and</p>
@@ -3392,7 +3392,7 @@ $$
 
 <p>and reordering we have</p>
 $$
-\boldsymbol{X}^T\boldsymbol{X}\boldsymbol{\beta})+\lambda sgn(\boldsymbol{\beta})=2\boldsymbol{X}^T(\boldsymbol{y}.
+\boldsymbol{X}^T\boldsymbol{X}\boldsymbol{\beta}+\lambda sgn(\boldsymbol{\beta})=2\boldsymbol{X}^T\boldsymbol{y}.
 $$
 
 <p>This equation does not lead to a nice analytical equation as in either Ridge regression or ordinary least squares. This equation can however be solved by using standard convex optimization algorithms using for example the Python package <a href="https://cvxopt.org/" target="_blank">CVXOPT</a>. We will discuss this later. </p>

doc/src/week35/week35.do.txt

@@ -2456,7 +2456,7 @@ For the sake of simplicity, let us assume that the design matrix is orthonormal,
 In this case the standard OLS results in 
 !bt
 \[
-\bm{\beta}^{\mathrm{OLS}} = \bm{X}^T\bm{y}=\sum_{i=0}^{p-1}\bm{u}_j\bm{u}_j^T\bm{y},
+\bm{\beta}^{\mathrm{OLS}} = \bm{X}^T\bm{y}=\sum_{i=0}^{n-1}\bm{u}_i\bm{u}_i^T\bm{y},
 \]
 !et
 
@@ -2504,7 +2504,7 @@ we have that the derivative of the cost function is
 and reordering we have
 !bt
 \[
-\bm{X}^T\bm{X}\bm{\beta})+\lambda sgn(\bm{\beta})=2\bm{X}^T(\bm{y}.
+\bm{X}^T\bm{X}\bm{\beta}+\lambda sgn(\bm{\beta})=2\bm{X}^T\bm{y}.
 \]
 !et
 This equation does not lead to a nice analytical equation as in either Ridge regression or ordinary least squares. This equation can however be solved by using standard convex optimization algorithms using for example the Python package "CVXOPT":"https://cvxopt.org/". We will discuss this later.