IN a study of the determinants of household expenditures on vacation travel, data were obtained from a sample of 2,246 households. The model estimated was:
logy = -4.054 + 1.1556 logX1 - 0.4408 logX2
(0.0546) (0.0490)
R^2 = 0.168
where
y= expenditure on vacation travel
x1 = total annual consumption expenditure
x2 = number of members in household
The numbers in parenthesis under the coefficients are the estimated coefficient standard errors.
a. Interpret the estimated regression coefficients.
b. Interpret the coefficient of determination.
c. All else being equal, find a 95% confidence interval for the percentage increase in expenditures on vacation travel resulting from a 1% increase in total annual consumption expenditures.
d. Assuming that the model is correctly specified, test , at the 1% significance level, the null hypothesis that, all else being equal, the number of members in a household does not affect expenditures on vacation travel against the alternative that the greater the number of household members, the lower the vacation travel expenditures.