Question: 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.

1. In the simple regression model
   \[\text { price }=\beta_{0}+\beta_{1} \text { assess }+u\]
   the assessment is rational if \(\beta_{1}=1\) and \(\beta_{0}=0 .\) The estimated equation is
   \[\begin{matrix} \widehat{price}=-14.47+.976\text{ assess } \\ (16.27) \\ n=88,\text{SSR}=165,644.51,{{R}^{2}}=.820 \\ \end{matrix}\]
   First, test the hypothesis that \(\mathrm{H}_{0}: \beta_{0}=0\) against the two-sided alternative. Then, test \(\mathrm{H}_{0}: \beta_{1}=1\) against the two-sided alternative. What do you conclude?
2. To test the joint hypothesis that \(\beta_{0}=0\) and \(\beta_{1}=1\), we need the SSR in the restricted model. This amounts to computing \(\sum_{i=1}^{\pi}\left(\text { price }_{i}-\text { assess }_{i}\right)^{2}\), where \(n=88\), since the residuals in the restricted model are just price \(_{i}\)
   - assess. (No estimation is needed for the restricted model because both parameters are specified under \(\mathrm{H}_{0}\).) This turns out to yield SSR = 209,448.99. Carry out the \(F\) test for the joint hypothesis.
3. Now, test \(\mathrm{H}_{0}: \beta_{2}=0, \beta_{3}=0\), and \(\beta_{4}=0\) in the model
   \[\text { price }=\beta_{0}+\beta_{1} \text { assess }+\beta_{2} \text { lotsize }+\beta_{3} s q r f t+\beta_{4} b d r m s+u\]
   The \(R\) -squared from estimating this model using the same 88 houses is .829.
4. If the variance of price changes with assess, lotsize, sqrft, or bdrms, what can you say about the \(F\) test from part (iii)?

Price: $2.99

Solution: The downloadable solution consists of 3 pages
Deliverable: Word Document