In Section 4-5, we used as an example testing the rationality of assessments of housing prices.

There, we used a log-log model in price and assess [see equation (4.47)]. Here, we use a level-level formulation.

(i) In the simple regression model price 5 b0 1 b1assess 1 u, the assessment is rational if b1 5 1 and b0 5 0. The estimated equation is price 5 214.47 1 .976 assess 116.272 1.0492 n 5 88, SSR 5 165,644.51, R2 5 .820.

First, test the hypothesis that H0: b0 5 0 against the two-sided alternative. Then, test H0: b1 5 1 against the two-sided alternative. What do you conclude?

(ii) To test the joint hypothesis that b0 5 0 and b0 5 1, we need the SSR in the restricted model.

This amounts to computing gn i51 1pricei 2 assessi 2 2

, where n 5 88, since the residuals in the restricted model are just pricei 2 assessi

. (No estimation is needed for the restricted model because both parameters are specified under H0.) This turns out to yield SSR 5 209,448.99.

Carry out the F test for the joint hypothesis.

(iii) Now, test H0: b2 5 0, b3 5 0, and b4 5 0 in the model price 5 b0 1 b1assess 1 b2lotsize 1 b3sqrft 1 b4bdrms 1 u.

The R-squared from estimating this model using the same 88 houses is .829.

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