Question

Exercise 54 Consider the null hypothesis Ho:B2 = B3 = 0 against the alternative Hu: B26= 0 and/or B36= 0, in the linear regression Ys= B1 + B2X42 + B3Xt3 + B4X4 + Suppose that you estimate the above model with a sample size of 64 observations. The residual sum of the squares is 397.2. You also estimate the restricted model under the null and the sum of squares of this restricted regression is 436.1. What would the conclusion of the hypothesis test be at the 5% significance level? (a) Reject the null hypothesis (b) Do not reject the null hypothesis C) Reject the alternative hypothesis (d) Cannot say Exercise 55 Which of these statements is a characteristic of the stepwise regression procedure? It chooses the jointly most important' explanatory variable from a set of candidate variables (IT) It can start with no variables in the regression and then it selects first the variable with the lowest p-value (11) It can start with no variables in the regression and then it selects first the variable with the highest p-value (a) I only (b) II only (c) III only (d) Both I and II

Answer 1

54) option b)

Don't reject H0

054) ftest o Restricted least squares option b.) F = (RSS R - RSSUR / m RSS R=436-1 - RSSR / (n-k) RSS UR = 397.2 m Restrictions = 2 n=64, k variables un unrestricted Regh = 4 80 F= (43601-397-2)/2 ~F2.60 Monts= 43601/60. F = 2.675 Now Foo5,2,60 = 3.15 as f calculated a f critical 80 don't Refect Ho. Ans

55) option a)

In stepwise regression, we start with basic model, & keep on adding variable till it turns out to be significant, with lower p values

This test whether added variables are jointly & individually significant or not