In studying the demand for farm tractors in the United States for the periods 1921€“1941 and 1948€“1957, Griliches€  obtained the following results:

where Y_t = 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 ˆ’ 1,and X₃ = interest rate prevailing in year t ˆ’ 1. The estimated standard errors are given in the parentheses.

a. Interpret the preceding regression.

b. Are the estimated slope coefficients individually statistically significant? Are they significantly different from unity?

c. Use the analysis of variance technique to test the significance of the overall regression.

d. How would you compute the interest-rate elasticity of demand for farm tractors?

e. How would you test the significance of estimated R²?

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R² = 0.793 0.519 log X21 – 4.933 log X34 (0.477) = constant logY, (0.231)