12.46 A study was done to determine whether the gender of the credit card holder was an important factor in generating profit for a certain credit card company. The variables considered were income, the number of family members, and the gender of the card holder. The data are as follows:

Family Profit Income Gender Members 522 78 5

−177 123 251

−56 453 288

−104 157

−181

−253 158 75 202

−451 146 89

−357 36750 42500 34250 36750 24500 27500 18000 24500 88750 19750 45000 55000 45800 38000 75000 99750 28000 39000 54350 32500 FFFFFFFFF MMMMMMMMMMM 13232111121243441211

(a) Fit a linear regression model using the variables available. Based on the fitted model, would the company prefer male or female customers?

(b) Would you say that income was an important factor in explaining the variability in profit?