Question: The data below were collected from a sample of 15 houses to develop a model for predicting assessed value (in $1000) based on the heating area (in thousands of square feet) and whether or not the house has a fire-place.

a. Fit a first-order model for y = assessed value, using heating area and fire-place availability as independent variables. Along with your other residual plots and scatter plots, plot a partial residual plot for Heating. You will have to create the partial residual plot (maybe in Excel), since Minitab does not do this.

b. Next, fit a model with an interaction term. Comment on the results. Use a test for nested models to verify your conclusion.

c. Finally, fit a model with the two first-order terms as well as Heating^2 (but no interaction term). Perform a test for nested models to determine whether this model is superior to the first-order model.