Question 2 [6 points]. For inferences regarding the mean response at a given value of the predictor variable, derive the sampling distribution of n = bo + bi Xhe (see bottom of Slide #27). Also, discuss the things that affect the variance in the sampling distribution. For what Xh is the variance the smallest? Question 3 [Regression for two-sample problems, 6 points). Let X denote a binary independent variable (with the values o and 1) and consider the simple linear regression model. Yij = Bo + B1Xij + Eij, ij ~ N(0,0%), Xij = i; i = 0,1; j = 1, 2, ..., ni Show that the OLS estimators for the intercept and slope are B =Yw, and =Y - Yo where ni j1 - Yij i = Y; = i= 0,1 Ni are the sample means for the dependent variable at X = 0 and X = 1, respectively. Write down the sampling distribution for the slope estimator in a simple form. Question 2 [6 points]. For inferences regarding the mean response at a given value of the predictor variable, derive the sampling distribution of n = bo + bi Xhe (see bottom of Slide #27). Also, discuss the things that affect the variance in the sampling distribution. For what Xh is the variance the smallest? Question 3 [Regression for two-sample problems, 6 points). Let X denote a binary independent variable (with the values o and 1) and consider the simple linear regression model. Yij = Bo + B1Xij + Eij, ij ~ N(0,0%), Xij = i; i = 0,1; j = 1, 2, ..., ni Show that the OLS estimators for the intercept and slope are B =Yw, and =Y - Yo where ni j1 - Yij i = Y; = i= 0,1 Ni are the sample means for the dependent variable at X = 0 and X = 1, respectively. Write down the sampling distribution for the slope estimator in a simple form