2. Suppose that a researcher collects data on houses that have sold in a particular neighborhood over the past year and obtains the regression results in table 2 below. The dependent variable is In( Price), the log of the price of the house; In(Size) is the log of the total size of the lot (in square feet); and Aircon is a dummy equal to 1 if the house has an air condoning system, and 0 otherwise. Using this data, he runs the model as specified above, and obtains the following results. Estimate Std. Error t value Pr(>|t[) (Intercept) 3.17 0.82 9.95 0.00 Aircon -0.84 0.61 -1.38 0.17 InSize 0.ZZZ 0.10 3.11 0.00 I(Aircon * InSize) 0.13 0.07 1.79 0.07 In answering the following questions, replace ZZZ with the last three digits of your student id number. i. How would you interpret the coefficient associated to In(Size)? ii. Suppose that Aircon is equal to zero and that Size = XXXX, where XXXX is first four digits of your student ID numbers. What is the expected change of an in- crease in Size of 1000-square-feet on Price? Construct a 95% confidence interval for the percentage change in price.iii. Now take Airmn equal to l and Size = 5000. What is the expected change in price of building a lsquarefoot addition to a house? Construct a 95% condence interval for the percentage change in price, knowing that the Couriflz, 3} = U. iv. Is the expected difference of an increase in Price for a house of EWU square feet with and without air conditioning statistically signicant at the 5% level? Explain