1. This question is about fitting a multiple linear regression to the response Y with 4 regressors X1, ..., X4. Some R-outputs are given below. Call : Im (formula = Y ~ X1 + X2 + X3 + X4) Coefficients : Estimate Std. Error t value Pr(>Itl) (Intercept) 0. 1863 5. 7957 0. 032 0.974463 X1 2. 2742 0. 5696 3.992 0. 000189 *** X2 1.9393 1. 3718 1. 414 0. 162871 X3 0. 1048 1. 3401 0. 078 0. 937942 X4 -0. 3171 0. 1378 -2.301 0. 025092 * Analysis of Variance Table Response : Y Df Sum Sq Mean Sq F value Pr (>F) X1 1 60. 1 60.1 0. 7093 0. 40321 X2 1 2747.3 2747.3 32. 4482 4. 496e-07 *** X3 1 3378.4 3378.4 39. 9016 4.333e-08 *** X4 1 448.1 5.2929 0. 02509 * Residuals 57 4826.1 84.7 (a) Construct a simpler ANOVA table for testing Ho : E(Y | X) = Bo vs H1 : E(Y | X) = Bo + BIX1 + ... + BAX4. Perform the test at significance level a = 0.05. (b) The first half of the R-outputs indicates that the term X1 is highly significant (by t-test), while the second half of the R-outputs indicates that this term is not significant (by F-test). Could you offer a possible explanation? (c) We are interested in conducting the test: Ho : 2 = 0; Bo, B1, B3, B4 arbitrary vs H1 : B2 # 0; Bo, B1, B3, B4 arbitrary. With the available R-outputs, is it possible to do this test? If yes, do the test at significance level a = 0.05; otherwise, just say no. (d) Construct a 95% confidence interval for B1 in the regression model E(Y | X) = Bo+BIXi+. ..+B4X4. (You need to extract related information from the R-outputs for the calculation of the CI.)