The Gilmore Accounting firm previously mentioned, in an effort to explain variation in client profitability, collected the data found in the file called Gilmore, where: y = Net profit earned from the client
x1 = Number of hours spent working with the client
x2 = Type of client:
1, if manufacturing
2, if service
3, if governmental
Gilmore has asked if it needs the client type in addition to the number of hours spent working with the client to predict the net profit earned from the client. You are asked to provide this information.
a. Fit a model to the data that incorporates the number of hours spent working with the client and the type of client as independent variables.
b. Fit a second-order model to the data, again using dummy variables for client type. Does this model provide a better fit than that found in part a? Which model would you recommend be used?