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 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 the scatterplots of the response variable versus the two explanatory variables as well as the scatterplot between the two explanatory variables. Do you notice any unusual features? Do the relevant plots appear straight enough for multiple regression?
B. Fit the multiple regression model to predict price of home from square feet and number of bathrooms) and summarize the estimates in the context of the problem.
C. What is the fraction of the variation of home prices that can be attributed to the explanatory variables? Is the fraction statistically significantly greater than zero?
D. Compare the partial slope (multiple regression) with the marginal slope (simple regression) for the number of bathrooms. Explain why they are very different and show a confidence interval for each.
E. What you predict the price should be for a home with 2 bathrooms that is 3,000 square feet? Find an approximate 95% prediction interval.