Question 4 (15pts) Suppose you estimate a simple regression of Y on X , Yi=l+2xi+u and obtain the following results: Estimate Std. Err. 15.1 2.73 0.36 0.05 Parameter :31 132 N = 500 You follow up by running a second regression that includes a variable Z: Yi = 151 + 2Xi + 5321' + U: obtaining the following results Parameter Estimate Std. Err. (31 15.1 5.54 132 0.34 0.15 ,33 1.45 2.68 N = 500 Based on the results of these two regressions, do you think that Z is an omitted variable? Do you think that Z is a redundant variable? Explain your answer, being sure to discuss the impacts of both an omitted variable (and the potential for bias) and of a redundant variable and which you think is the case here. Question 5 (10pts) Consider the following regression: Y1: = :51 + 19in + 5321' + 54W + (35-41: + Us You wish to test the linear restriction ,83 + ; = c. Explain how to regroup variables in order to be able to test this linear restriction and show the regression equation you'd use. Be sure to note what sort of test (t or F) you should use to do so