12.57 An agricultural economist believes that the amount of fish consumed (y) in tons in a year in the France depends on the price of fish 1x12 in euros per pound, the price of potatoes 1x22 in euros per pound, the price of chicken 1x32 in euros per pound, and the income per household 1x42 in thousands of euros. The following sample regression was obtained through least squares, using 30 annual observations:

log y = -0.018 - 0.536 10.1722 log x1 + 0.208 10.0982 log x2

+ 0.205 10.1212 log x3 + 0.425 10.1332 log x4 R2 = 0.771

a. Interpret the coefficient on log x1.

b. Interpret the coefficient on log x2.

c. Test, at the 1% significance level, the null hypothesis that the coefficient on log x4 in the population regression is 0 against the alternative that it is positive.

d. Test the null hypothesis that the four variables 1log x1, log x2, log x3, log x42 do not, as a set, have any linear influence on log y.

e. The economist is also concerned that, over the years, the increasing awareness of the effects of fish consumption on health may have influenced the demand for fish. If this is indeed the case, how would this influence your view of the original estimated regression?