In order to help clients determine the price at which their house is likely to sell, a realtor gathered a sample of 150 purchase transactions in her area during a recent three-month period. For the response in the model, use the price of the home (in thousands of dollars). As explanatory variables, use the number of square feet (also in thousands) and the number of bathrooms.
(a) Examine scatterplots of the response versus the two explanatory variables as well as the scatterplot between the explanatory variables. Do you notice any unusual features in the data? Do the relevant plots appear straight enough for multiple regression?
(b) Fit the indicated multiple regression and show a summary of the estimated features of the model.
(c) Does the estimated model appear to meet the conditions for the use of the MRM?
(d) Does this estimated model explain statistically significant variation in the prices of homes?
(e) Compare the marginal slope for the number of bathrooms to the partial slope. Explain why these are so different, and show a confidence interval for each.
(f) A homeowner asked the realtor if she should spend $40,000 to convert a walk-in closet into a small bathroom in order to increase the sale price of her home. What does your analysis indicate?