The data file stockton5_small contains observations on 1200 houses sold in Stockton, California, during 1996-1998. [Note: The data file stockton5 includes 2610 observations.]. Scale the variable SPRICE to units of \(\$ 1000\), by dividing it by 1000 .

a. Estimate the regression model SPRICE \(=\beta_{1}+\beta_{2}\) LIVAREA \(+e\) using only houses that are on large lots. Repeat the estimation for houses that are not on large lots. Finally, estimate the regression using data on both large and small lots. Interpret the estimates. How do the estimates compare?

b. Estimate the regression model SPRICE \(=\alpha_{1}+\alpha_{2}\) LIVAREA \(^{2}+e\) using only houses that are on large lots. Repeat the estimation for houses that are not on large lots. Interpret the estimates. How do the estimates compare?

c. Estimate a linear regression SPRICE \(=\eta_{1}+\eta_{2}\) LGELOT \(+e\) with dependent variable SPRICE and independent variable the indicator \(L G E L O T\), which identifies houses on larger lots. Interpret these results.

d. If the estimates in part (a) and/or part (b) differ substantially for the large lot and small lot subsamples, will assumption SR1 be satisfied in the model that pools all the observations together? If not, why not? Do the results in (c) offer any information about the potential validity of SR1?