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 (x₁) in euros per pound, the price of potatoes (x₂) in euros per pound, the price of chicken (x₃) in euros per pound, and the income per household (x₄) in thousands of euros. The following sample regression was obtained through least squares, using 30 annual observations:

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 (log x₁, log x₂, log x₃, log x₄) 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?

Transcribed Image Text:

log y = -0.018- 0.536 log x₁ + 0.208 log x₂ (0.172) (0.098) + 0.205 log x3 + 0.425 log x4 (0.121) (0.133) R² = 0.771