Consider the following model that estimate the rationality of assessments of housing prices, price = ß0 + ß1 assess + u.

The assessment is rational if ß1 = 1 and ß0 = 0. The estimated equation is

price = -14.47 + 0.976 assess

(16.27) (0.049)

n = 88, R2 = 0.820, SSR = 165,644.51

(i) Test the hypothesis that H0 : ß0 = 0 against the two sided alternatives. Then, test H0: ß1= 1 against the two sided alternatives. What do you conclude?

(ii) To test the joint hypothesis that and , we need the SSR in the restricted model. This amount to computing

?ni=1 ( price i – assess i )2 , where n = 88, since the residuals in the restricted model are just (price i – assess i ). [No estimation is needed for the restricted model because both parameters are specified under H0.] This turns out to yield SSR = 209,448.99. Carry out the F test for the joint hypothesis.

(iii) Now, test H0 : ß2 = 0, ß3 = 0, and ß4 = 0 in the model

price = ß0 + ß1 assess + ß2 lotsiz + ß3 sqrft + ß4 bdrmsl + u,

with R2 = 0.829.

If the variance of price change with assess, lotsize, sqrft, or bdrms, what can you say about the F test from part (iii)?