An agricultural economist believes that the amount of beef consumed (y) in tons in a year in the United States depends on the prices of beef (x1) in dollars per pound, the price of pork (X2) in dollars per pound, the price of chicken (X3) in dollars per pound, and the income per household (X4) in thousands of dollars. The following sample regression was obtained through least squares,m using 30 annual observations:

logy = -0.024 - 0.529logX1 + 0.217logx2 + 0.193logx3 + 0.414 logX4 R^2 = 0.683
(0.168) (0.103) (0.106) (0.163)

the numbers in parenthesis under the coefficients are estimated coefficient standard errors.

a. Interpret the coefficient on logX1.

b. Interpret the coefficient on logX2.

c. Test, at the 1% significance level, the null hypothesis that the coefficient on logX4 in the population regression is 0 against the alternative that it is positive.

d. Test the null hypothesis that the four variables (logX1, logX2, logX3, logX4) 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 heavy red meat consumption on health may have influenced the demand for beef. If this is indeed the case, how would this influence your view of the original estimated regression.