A study is done in an attempt to relate personal savings to personal income (in billions of dollars) for the time period from 1935 to 1954. The data are given in Table P-18.

a. Fit a simple linear regression model to the data in Table P-18 using per- sonal income to predict personal savings. Specifically: (1) Test for the sig- nificance of the regression slope coefficient at the a = .01 level; (2) test for the significance of the regression using the F test (at a = .01); (3) calculate and interpret this quantity; and (4) test for autocorrelation (at a = .05). Should you modify your conclusions in parts 1 and 2? How can the model be improved?

b. Construct a dummy variable X2 for the war years. Let X2 = 0 for peacetime and X2 = 1 for wartime. The war years are from 1941 to 1945. Fit a multi- ple linear regression model using personal income and the war years dummy variable as predictor variables for personal savings. Evaluate the results. Specif- ically: (1) Test to determine whether knowledge of the war years makes a significant contribution to the prediction of personal savings beyond that pro- vided by personal income (set a = .01); and (2) test for autocorrelation. Is the multiple regression model better than the simple linear regression model of part a? Discuss.