The following data show the real price of butter and real incomes, to supplement the data in Problem 7.2.

(a) Estimate a multiple regression model of the demand for margarine. Do the coefficients have the expected signs?

(b) Test the significance of the individual coefficients and of the regression as a whole.

(c) Should the model be simplified?

(d) Calculate the elasticity of demand. How does it differ from your earlier answer?

(e) Estimate the cross-price demand elasticity.

(f ) Should other variables be added to improve the model, in your view?

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Year Price of butter Real income Year Price of butter Real income 1970 105.5 70.3 1980 119.2 92.1 1971 130.9 71.1 1981 114.2 91.4 1972 131.9 77.1 1982 114.5 90.9 1973 99.5 82.1 1983 110.0 93.3 1974 89.6 81.5 1984 107.9 96.8 1975 92.1 81.9 1985 100.0 100.0 1976 109.1 81.7 1986 104.2 104.5 1977 118.2 79.9 1987 99.8 108.1 1978 123.4 85.8 1988 100.2 114.6 1979 130.6 90.7