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: P rice i = 40 (29) + 35 (5.0) LOTi + 2.0 (1.1) AGEi + 10.0 (10.0) BEDi + 4.0 (3.0) EIREi + 100 (9.0) BEACHi where n = 30, R2 = 0.63, and P RICEi = the price of the i th house (in thousands of dollars), LOTi = the size of the lot of the i th house (in thousands of square feet), AGEi = the age of the i th house in years, BEDi = the number of bedrooms in the i th house, F IREi =a dummy variable for a fireplace ( 1 = yes for the i th house), and BEACHi = a dummy for having beach frontage ( 1 = yes for the i th 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.