# Question

An agricultural economist believes that the amount of beef consumed (y) in tons in a year in the United States depends on the price 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, using 30 annual observations:

The numbers in parentheses under the coefficients are the estimated coefficient standard errors.

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 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?

The numbers in parentheses under the coefficients are the estimated coefficient standard errors.

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 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?

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