typo in hw 1

doc/Projects/2018/hw1/html/hw1-bs.html

@@ -120,7 +120,7 @@ MathJax.Hub.Config({
 <center><b>Department of Physics, University of Oslo, Norway</b></center>
 <br>
 <p>
-<center><h4>Aug 27, 2018</h4></center> <!-- date -->
+<center><h4>Aug 30, 2018</h4></center> <!-- date -->
 <br>
 <p>
 </div> <!-- end jumbotron -->
@@ -245,12 +245,12 @@ Discuss the meaning of these results. Try also to vary the coefficient in front
 Show that the variance of the parameters \( \beta \) in the linear regression method (chapter 3, equation (3.8) of <a href="https://www.springer.com/gp/book/9780387848570" target="_self">Trevor Hastie, Robert Tibshirani, Jerome H. Friedman, The Elements of Statistical Learning, Springer</a>) is given as 
 
 $$
-mathrm{Var}(\hat{\beta}) = \left(\hat{X}^T\hat{X}\right)^{-1}\sigma^2,
+\mathrm{Var}(\hat{\beta}) = \left(\hat{X}^T\hat{X}\right)^{-1}\sigma^2,
 $$
 
 with 
 $$
-\sigma^2 = \frac{1}{N-p-1}\sum_{i=1}{N} (y_i-\tilde{y}_i)^2,
+\sigma^2 = \frac{1}{N-p-1}\sum_{i=1}^{N} (y_i-\tilde{y}_i)^2,
 $$
 
 where we have assumed that we fit a function of degree \( p-1 \) (for example a polynomial in \( x \)). 

doc/Projects/2018/hw1/html/hw1.html

@@ -86,7 +86,7 @@ MathJax.Hub.Config({
 <center><b>Department of Physics, University of Oslo, Norway</b></center>
 <br>
 <p>
-<center><h4>Aug 27, 2018</h4></center> <!-- date -->
+<center><h4>Aug 30, 2018</h4></center> <!-- date -->
 <br>
 
 <h2 id="___sec0">Exercise 1  </h2>
@@ -209,12 +209,12 @@ Discuss the meaning of these results. Try also to vary the coefficient in front
 Show that the variance of the parameters \( \beta \) in the linear regression method (chapter 3, equation (3.8) of <a href="https://www.springer.com/gp/book/9780387848570" target="_blank">Trevor Hastie, Robert Tibshirani, Jerome H. Friedman, The Elements of Statistical Learning, Springer</a>) is given as 
 
 $$
-mathrm{Var}(\hat{\beta}) = \left(\hat{X}^T\hat{X}\right)^{-1}\sigma^2,
+\mathrm{Var}(\hat{\beta}) = \left(\hat{X}^T\hat{X}\right)^{-1}\sigma^2,
 $$
 
 with 
 $$
-\sigma^2 = \frac{1}{N-p-1}\sum_{i=1}{N} (y_i-\tilde{y}_i)^2,
+\sigma^2 = \frac{1}{N-p-1}\sum_{i=1}^{N} (y_i-\tilde{y}_i)^2,
 $$
 
 where we have assumed that we fit a function of degree \( p-1 \) (for example a polynomial in \( x \)). 

doc/Projects/2018/hw1/pdf/hw1.p.tex

@@ -155,7 +155,7 @@ Homework 1
 
 % --- begin date ---
 \begin{center}
-Aug 27, 2018
+Aug 30, 2018
 \end{center}
 % --- end date ---
 
@@ -282,11 +282,11 @@ Discuss the meaning of these results. Try also to vary the coefficient in front
 Show that the variance of the parameters $\beta$ in the linear regression method (chapter 3, equation (3.8) of \href{{https://www.springer.com/gp/book/9780387848570}}{Trevor Hastie, Robert Tibshirani, Jerome H. Friedman, The Elements of Statistical Learning, Springer}) is given as 
 
 \[
-mathrm{Var}(\hat{\beta}) = \left(\hat{X}^T\hat{X}\right)^{-1}\sigma^2,
+\mathrm{Var}(\hat{\beta}) = \left(\hat{X}^T\hat{X}\right)^{-1}\sigma^2,
 \]
 with 
 \[
-\sigma^2 = \frac{1}{N-p-1}\sum_{i=1}{N} (y_i-\tilde{y}_i)^2,
+\sigma^2 = \frac{1}{N-p-1}\sum_{i=1}^{N} (y_i-\tilde{y}_i)^2,
 \]
 where we have assumed that we fit a function of degree $p-1$ (for example a polynomial in $x$). 
 

doc/Projects/2018/hw1/pdf/hw1.tex

@@ -125,7 +125,7 @@ Homework 1
 
 % --- begin date ---
 \begin{center}
-Aug 27, 2018
+Aug 30, 2018
 \end{center}
 % --- end date ---
 
@@ -252,11 +252,11 @@ Discuss the meaning of these results. Try also to vary the coefficient in front
 Show that the variance of the parameters $\beta$ in the linear regression method (chapter 3, equation (3.8) of \href{{https://www.springer.com/gp/book/9780387848570}}{Trevor Hastie, Robert Tibshirani, Jerome H. Friedman, The Elements of Statistical Learning, Springer}) is given as 
 
 \[
-mathrm{Var}(\hat{\beta}) = \left(\hat{X}^T\hat{X}\right)^{-1}\sigma^2,
+\mathrm{Var}(\hat{\beta}) = \left(\hat{X}^T\hat{X}\right)^{-1}\sigma^2,
 \]
 with 
 \[
-\sigma^2 = \frac{1}{N-p-1}\sum_{i=1}{N} (y_i-\tilde{y}_i)^2,
+\sigma^2 = \frac{1}{N-p-1}\sum_{i=1}^{N} (y_i-\tilde{y}_i)^2,
 \]
 where we have assumed that we fit a function of degree $p-1$ (for example a polynomial in $x$). 
 

doc/src/Projects/2018/Exercises/hw1.do.txt

@@ -105,13 +105,13 @@ Show that the variance of the parameters $\beta$ in the linear regression method
 
 !bt
 \[
-mathrm{Var}(\hat{\beta}) = \left(\hat{X}^T\hat{X}\right)^{-1}\sigma^2,
+\mathrm{Var}(\hat{\beta}) = \left(\hat{X}^T\hat{X}\right)^{-1}\sigma^2,
 \]
 !et
 with 
 !bt
 \[
-\sigma^2 = \frac{1}{N-p-1}\sum_{i=1}{N} (y_i-\tilde{y}_i)^2,
+\sigma^2 = \frac{1}{N-p-1}\sum_{i=1}^{N} (y_i-\tilde{y}_i)^2,
 \]
 !et
 where we have assumed that we fit a function of degree $p-1$ (for example a polynomial in $x$).