Based on 11 annual observations, the following regressions were obtained:
Model A: Y(sub t) = 2.6911 - 0.4795X(sub t)
se = (.1216) (.1140) r^2 = .6628
Model B: Y(sub t) = 0.7774 - .2530 ln X(sub t)
se = (.0152) (0.0494) r^2 = 0.7448
where Y = the cups of coffee consumed per person per day and X = the price of coffee, dollars per pound.
a. interpret the slope coefficients in the two models. explain specifically.
b. you are told that Y(mean) = 2.43 and X(mean) = 1.11. At these mean values, estimate the price elasticity for model A and show work.
c. what is the price elasticity for model B? show work
d. from the estimated elasticities, can you say that the demand for coffee is price inelastic? why?
e. how would you interpret the intercept in model B? (hint take the anitlog) show work
f. "since the r^2 of model B is larger that that of model A, model B is preferable to model A." COMMENT.