8.12 Fair market value of Hawaiian properties. Prior to 1980, private homeowners in Hawaii had to ease the land their homes were built on because the law (dating back to the islands' feudal period) required that land be owned only by the big estates. After 1980, however, a new law instituted condemnation proceedings so that citizens could buy their own land. To comply with the 1980 law, one large Hawaiian estate wanted to use regression analysis to estimate the fair market value of its land. Its first proposal was the quadratic model E(y) = Bo + Pix + 82X : where y = Leased fee value (i.e., sale price of property) * = Size of property in square feet SHAWAII LEASED FEE VALUE y. thousands SIZE PROPERTY of dollan 4. thousands 70.7 13.5 52.7 9.6 87.6 17.6 412 7.9 11.5 45.1 86.8 15.2 73.3 12.0 1443 13.8 10 613 10.0 11 148.0 145 12 85.0 102 13 171.2 14 97 5 132 158.1 163 16 74.2 12.3 470 2.7 54.7 09 68.0 11.2 75.2 Data collected for 20 property sales in a particular neighborhood, given in the table above, were used to fit the model. The least squares prediction equation is y = -44.0947 + 11.5339 x - .06378 x : (a) Calculate the predicted values and corresponding residuals for the model. (b) Plot the residuals versus y". Do you detect any trends? If so, what does the pattern suggest about the model? (c) Conduct a test for heteroscedasticity. [Hint: Divide the data into two subsamples, x = 12 andx > 12, and fit the model to both subsamples.] (d) Based on your results from parts b and c, how should the estate proceed? 8.21 Fair market value of Hawaiian properties. Refer to Exercise 8.12. (p. 407) and the data saved in the HAWAII file. Use one of the graphical techniques described in this section to check the normality assumption. 8.36 Life insurance policies in force. The next table represents all life insurance policies (in millions) in force on the lives of U.S. residents for the years 1980 through 2006. (a) Fit the simple linear regression model, E(Y:) = Bo + Bit , to the data for the years 1980 to 2006 (t = 1, 2, . . . . 27). Interpret the results. (b) Find and plot the regression residuals against t. Does the plot suggest the presence of autocorrelation? Explain. (c) Conduct the Durbin-Watson test (at o = .05) to test formally for the presence of positively