1.6 We used the data in MEAP93.RAW for Example 2.12. Now we want to explore the relationship between the math pass rate (matth) and spending per student (expend). (i) Do you think each additional dollar spent has the same effect on the pass rate, or does a diminishing effect seem more appropriate? Explain. (ii) In the population model mathIO = 30 + Bllog(expend) + u, argue that 31/10 is the percentage point change in mathIO given a 10% increase in expend. (iii) Use the data in MEAP93.RAW to estimate the model from part (ii). Report the estimated equation in the usual way, including the sample size and Rsquared. (iv) How big is the estimated spending effect? Namely, if spending increases by 10%, what is the estimated percentage point increase in mathJO? (v) One might worry that regression analysis can produce tted values for math] 0 that are greater than 100. Why is this not much of a worry in this data set? 1.7 Use the data in HPRICEIRAW to estimate the model price = 30 + [31qu + zbdrms + u, where price is the house price measured in thousands of dollars. (i) Write out the results in equation form. (ii) What is the estimated increase in price for a house with one more bedroom, hold ing square footage constant? (iii) What is the estimated increase in price for a house with an additional bedroom that is 140 square feet in size? Compare this to your answer in part (ii). (iv) What percentage of the variation in price is explained by square footage and num ber of bedrooms? (v) The rst house in the sample has sqrft = 2,438 and bdrms = 4. Find the predicted selling price for this house from the OLS regression line. (vi) The actual selling price of the rst house in the sample was $300,000 (so price = 300). Find the residual for this house. Does it suggest that the buyer underpaid or overpaid for the house