Caveat Emptor, Inc. is a home inspection service that provides prospective home buyers with a thorough assessment of the major systems in a house prior to the execution of the purchase contract. Prospective home buyers often ask the company for an estimate of the average monthly heating cost of the home during the winter. To answer this question, the company wants to build a regression model to help predict the average monthly heating cost (Y) as a function of the average outside temperature in winter (X1), the amount of attic insulation in the house (X2), the age of the furnace in the house (X3), and the size of the house measured in square feet (X4). Data on these variables for a number of homes was collected and may be found in the file Dat9-20.xls on your data disk.

a. Prepare scatter plots showing the relationship between the average heating cost and each of the potential independent variables. What sort of relationship does each plot suggest?

b. If the company wanted to build a regression model using only one independent variable to predict the average heating cost of these houses, what variable should be used?

c. If the company wanted to build a regression model using only two independent variables to predict the average heating cost of these houses, what variables should be used?

d. If the company wanted to build a regression model using only three independent variables to predict the average heating cost of these houses, what variables should be used?

e. Suppose the company chooses to use the regression function with all four independent variables. What is the estimated regression function?

f. Suppose the company decides to use the model with the highest adjusted R2 statistic. Develop a 95% prediction interval for the average monthly heating cost of a house with 4 inches of attic insulation, a 5-year-old furnace, 2500 square feet, and in a location with an average outside winter temperature of 40. Interpret this interval.