Although the time series data in Table P-18 are old, they provide the basis for some interesting regression modeling. Using the data in Table P-18, attempt to relate personal savings to personal income (in billions of dollars) for the time period from 1935 to 1954.

a. Fit a simple linear regression model to the data in Table P-18, using personal income to predict personal savings. (1) Test for the significance of the regression at the α = .01 level; (2) calculate r2, and interpret this quantity; and (3) test for autocorrelation using the Durbin-Watson test with α = .05. Should you modify your conclusion in part 1? How can the model be improved?
b. Construct a dummy variable, X2, for the WWII years. Let X2 = 0 for peacetime and X2 = 1 for wartime. The war years are from 1941 to 1945. Fit a multiple linear regression model using personal income and the war years dummy variable as predictor variables for personal savings. Evaluate the results. Specifically (1) test to determine whether knowledge of the war years makes a significant contribution to the prediction of personal savings beyond that provided by personal income (set α = .01) and (2) test for autocorrelation. Is the multiple regression model better than the simple linear regression model of part a? Discuss.

TABLE P-18 Personal Savings Y Personal Income X Personal Personal Savings Y Income X | Year Savings Y Personal Personal Income X Year Year 1935 1936 1937 1938 1939 1940 1941 60 1942 28 1943 1944 1945 1946 1947 1948 123 1949 151 1950 13 165 1951 171 952 179 1953 20 191 1954 9 210 207 279 257 273 288 69 74 18 19 30 73 78