Homework problem.

Again consider the regression Y = Bo+ BIX1+ 82X2 + B3X3 + E Let X = [1, X1, X2, X3] and B = [Bo, B1, 82, 83]. Suppose that X is not perfectly colinear, the variance of X is finite and not zero, and you have iid observations (Y1, X1), . .., (YN, XN) 1. Write down the sample minimization problem that the OLS estimator for 8 solves 2. We know VN(3 - B) 4 N(0, E). Give a consistent estimator for _ 3. Construct a test for Ho : B1 = 0 versus HA : B1 # 0 at the 1% significance level (specify the test statistic, critical value, and rejection rule) 4. Construct a test for Ho : B1 = 282 versus HA : B1 / 282 at the 5% significance level (specify the test statistic, critical value, and rejection rule) 5. Construct a 95% confidence interval for 81 - B2