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. Plot house selling price SPRICE against house living area for all houses in the sample.

b. Estimate the regression model SPRICE \(=\beta_{1}+\beta_{2}\) LIVAREA \(+e\) for all the houses in the sample. Interpret the estimates. Draw a sketch of the fitted line.

c. Estimate the quadratic model SPRICE \(=\alpha_{1}+\alpha_{2}\) LIVAREA \(^{2}+e\) for all the houses in the sample. What is the marginal effect of an additional 100 square feet of living area for a home with 1500 square feet of living area.

d. In the same graph, plot the fitted lines from the linear and quadratic models. Which seems to fit the data better? Compare the sum of squared residuals (SSE) for the two models. Which is smaller?

e. If the quadratic model is in fact "true," what can we say about the results and interpretations we obtain for the linear relationship in part (b)?