# Hw2 - PS 233 Intermediate Statistical Analysis Homework 2(Due Exercise 1 For the simple linear regression model y i = 0 1 x1i ei show that the

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PS 233 – Intermediate Statistical Analysis Homework 2 (Due 2/13/2002) Exercise 1 For the simple linear regression model – i i i e x y + + = 1 1 0 β – show that the square of the t-statistics used in testing 0 1 = is numerically equivalent to the F- statistics in the analysis of variance table, that is, show that MSE SSreg = 2 1 1 ) r( a ˆ v ˆ , where SSreg is the regression (or explained) sum of squares ( hint: how many degrees of freedom are associated with this quantity? ), and MSE is equal to unexplained sum of squares divided by its degrees of freedom. Exercise 2 In testing the null hypothesis 0 H : 0 1 = versus the alternative hypothesis 1 H : 0 1 in a simple linear regression model – i i i e x y + + = 1 1 0 – show that the p-values obtained from the t-test are equivalent to the p-values obtained under an F-test . Exercise 3 Show that

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( 29 ( 29 y X y y X y X y ˆ ˆ ˆ β - = - - Exercise 4 Let z = Ay
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## This note was uploaded on 10/21/2011 for the course PS 233 taught by Professor Staff during the Spring '11 term at Duke.

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Hw2 - PS 233 Intermediate Statistical Analysis Homework 2(Due Exercise 1 For the simple linear regression model y i = 0 1 x1i ei show that the

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