From 30c06f12459255fe66c30d83834f971a7074acd7 Mon Sep 17 00:00:00 2001 From: mhjensen Date: Thu, 30 Aug 2018 06:27:10 +0200 Subject: [PATCH] typo in hw 1 --- doc/Projects/2018/hw1/html/hw1-bs.html | 6 +++--- doc/Projects/2018/hw1/html/hw1.html | 6 +++--- .../2018/hw1/ipynb/ipynb-hw1-src.tar.gz | Bin 206 -> 207 bytes doc/Projects/2018/hw1/pdf/hw1.p.tex | 6 +++--- doc/Projects/2018/hw1/pdf/hw1.pdf | Bin 195815 -> 195373 bytes doc/Projects/2018/hw1/pdf/hw1.tex | 6 +++--- doc/src/Projects/2018/Exercises/hw1.do.txt | 4 ++-- 7 files changed, 14 insertions(+), 14 deletions(-) diff --git a/doc/Projects/2018/hw1/html/hw1-bs.html b/doc/Projects/2018/hw1/html/hw1-bs.html index 829932ef6..2b32af321 100644 --- a/doc/Projects/2018/hw1/html/hw1-bs.html +++ b/doc/Projects/2018/hw1/html/hw1-bs.html @@ -120,7 +120,7 @@ MathJax.Hub.Config({
Department of Physics, University of Oslo, Norway

-

Aug 27, 2018

+

Aug 30, 2018


@@ -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 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 \( x \)). diff --git a/doc/Projects/2018/hw1/html/hw1.html b/doc/Projects/2018/hw1/html/hw1.html index adb5658c6..64a4c3ea1 100644 --- a/doc/Projects/2018/hw1/html/hw1.html +++ b/doc/Projects/2018/hw1/html/hw1.html @@ -86,7 +86,7 @@ MathJax.Hub.Config({

Department of Physics, University of Oslo, Norway

-

Aug 27, 2018

+

Aug 30, 2018


Exercise 1

@@ -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 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 \( x \)). diff --git a/doc/Projects/2018/hw1/ipynb/ipynb-hw1-src.tar.gz b/doc/Projects/2018/hw1/ipynb/ipynb-hw1-src.tar.gz index 875d6394b11a266d6b49a5d3d37a17dae3f7eff9..c1f90dfe804cf04cdabe4056cdf1fe12c35c5cf0 100644 GIT binary patch literal 207 zcmb2|=3rngYL8}MetZ6W7L%dC@xt?VM{N#H+VQ$d@5RC90Izt3O&g{EtK3$(^zQa+ ztrsWnEtyhhKV9CK=kS@^k5czViTt$gpXa6-8a|cBa`p1*A(OLf7k+gqi45B{FLUX# zMQw{@I;-w^mLH$uYcu~+-dg`__H(TJbIt7E?A)ic{g3j!=;A$JeEiPqD+wCzqkGj$lyV}B_sC_tJw@1 G3=9Bc_F#tq literal 206 zcmb2|=3sc~*AmUZ{Pz68EG9#NV}Hq)$ diff --git a/doc/Projects/2018/hw1/pdf/hw1.p.tex b/doc/Projects/2018/hw1/pdf/hw1.p.tex index 57890b7ac..e5bdf40f9 100644 --- a/doc/Projects/2018/hw1/pdf/hw1.p.tex +++ b/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 $x$). diff --git a/doc/Projects/2018/hw1/pdf/hw1.pdf b/doc/Projects/2018/hw1/pdf/hw1.pdf index 832626724bf2527f925fb802a735f656651a9927..8cc4217006789ab3eef360928f924d4d89096c99 100644 GIT binary patch delta 50337 zcmV)2K+M1A`3tS~3$Td+0Zg-s0rUq1K@`#kvw{hr3j#1Rmk|vCD1WV3OOM+&5Wf3Y z@F)Wj!?(y5y%f!(K@lKXqiB&$0mas?h1!xM$?@)`zrDkkEPAz@MbVQeYB-ONGsBM} z=oS(5WFp~@%bk_e0 zB6=c{6Rfm|68Byri9=(lcoZo688f+%m}`x4PO#?2OI{PE9<#?U>?PVXCd5R6pR53) z5C#P(aS^psJHL3fT6|qlkR^yBW(rIVNHLAIR%pFneELk#27f-jLj-f9(aDMKk;L#q z&<l1V1FwS?d(E~HF%%Ot^R 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b/doc/Projects/2018/hw1/pdf/hw1.tex index 9b7b511d6..c722cb8e3 100644 --- a/doc/Projects/2018/hw1/pdf/hw1.tex +++ b/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 $x$). diff --git a/doc/src/Projects/2018/Exercises/hw1.do.txt b/doc/src/Projects/2018/Exercises/hw1.do.txt index 7e9b014c6..08c3d6adf 100644 --- a/doc/src/Projects/2018/Exercises/hw1.do.txt +++ b/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 $x$).