In studying the demand for farm tractors in the United States for the pe- riods 1921-1941 and 1948-1957, Griliches† obtained the following results:
logYt = constant - 0.519 log X2t - 4.933 log X3t R2 = 0.793 (0.231) (0.477)
where Yt = value of stock of tractors on farms as of January 1, in 1935-1939 dollars, X2 = index of prices paid for tractors divided by an index of prices received for all crops at time t - 1, X3 = interest rate pre- vailing in year t - 1, and the estimated standard errors are given in the parentheses.
a. Interpret the preceding regression.
b. Are the estimated slope coef?cients individually statistically signi?- cant? Are they signi?cantly different from unity?
c. Use the analysis of variance technique to test the signi?cance of the overall regression. Hint: Use the R2 variant of the ANOVA technique.
d. How would you compute the interest-rate elasticity of demand for farm tractors?
e. How would you test the signi?cance of estimated R2?