Problem 1 Suppose that you estimate a model of house prices to determine the impact of having beach frontage on the value of a house. After researching the problem, you decide to use the size of the lot instead of the size of the house as your explanatory variable for a. number of theoretical and data availability reasons. The results (standard errors in parentheses ) are : Price, = 40 + 35 LOT, + -2.0AGE , + 10.0 BED, + -4.0EIRE, + 100 BEACH (29 ) (5.0) (1.1) (10 .0) (a.0) (9.0) where n = 30, R2 = 0.63, and PRICE, = the price of the ith house (in thousands of dollars ), LOT, = the size of the lot of the ith house (in thousands of square feet ), AGE , = the age of the ith house in years, BED = the number of bedrooms in the ith house FIRE, =a dummy variable for a fireplace ( 1 = yes for the h house ), and BEACH, = a dummy for having beach frontage ( 1 = yes for thath house ). a You expect the variables LOT, BED, and BEACH to have positive coefficients. Test each of these hypotheses at the 5 percent level . b You expect AGE to have a negative coefficient. Test this hypothesis at the 10 percent level. c At first you expect FIRE to have a positive coefficient, but one of your friends says that fireplaces are messy and are a pain to keep clean, so you are not sure. Run a two-sided t-test around zero to test the two-sided hypothesis at the 5 percent level. Problem 2 Using the EAEF data set , regress LGEARN on S, EXP, and ASVABC. Use F-tests to determine whether the coefficients on S and EXP are