Refer to the energy demand data given in Table 5-3. Instead of fitting the log-linear model to the data, fit the following linear model:
Yt = B1 + B2X2t + B3X3, + ut
a. Estimate the regression coefficients, their standard errors, and obtain R2 and adjusted R2.
b. Interpret the various regression coefficients
c. Are the estimated partial regression coefficients individually statistically significant? Use the p values to answer the question.
d. Set up the ANOVA table and test the hypothesis that B2 = B3 = 0.
e. Compute the income and price elasticities at the mean values of Y, X2, and X3. How do these elasticities compare with those given in regression (5.12)?
f. Using the procedure described in Problem 5.16, compare the R2values of the linear and log-linear regressions. What conclusion do you draw from these computations?
g. Obtain the normal probability plot for the residuals obtained from the linear-in-variable regression above. What conclusions do you draw?
h. Obtain the normal probability plot for the residuals obtained from the log-linear regression (5.12) and decide whether the residuals are approximately normally distributed.
i. If the conclusions in (g) and (h) are different, which regression would you choose and why?