The data file collegetown contains observations on 500 single-family houses sold in Baton Rouge, Louisiana, during 2009-2013. The data include sale price (in thousands of dollars), PRICE, and total interior area of the house in hundreds of square feet, SQFT.

a. Plot house price against house size in a scatter diagram.

b. Estimate the linear regression model PRICE \(=\beta_{1}+\beta_{2} S Q F T+e\). Interpret the estimates. Draw a sketch of the fitted line.

c. Estimate the quadratic regression model PRICE \(=\alpha_{1}+\alpha_{2} S Q F T^{2}+e\). Compute the marginal effect of an additional 100 square feet of living area in a home with 2000 square feet of living space.

d. Graph the fitted curve for the model in part (c). On the graph, sketch the line that is tangent to the curve for a 2000 -square-foot house.

e. For the model in part (c), compute the elasticity of PRICE with respect to SQFT for a home with 2000 square feet of living space.

f. For the regressions in (b) and (c), compute the least squares residuals and plot them against SQFT. Do any of our assumptions appear violated?

g. One basis for choosing between these two specifications is how well the data are fit by the model. Compare the sum of squared residuals (SSE) from the models in (b) and (c). Which model has a lower SSE? How does having a lower SSE indicate a "better-fitting" model?