1. 8 pts. 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 credit card holder. The data are as follows: profit Income gender 157 -181 -253 158 75 202 -451 146 89 -357 522 78 5 -177 123 251 -56 453 288 -104 45000 55000 45800 38000 75000 99750 28000 39000 54350 32500 36750 42500 34250 36750 24500 27500 18000 24500 88750 19750 M M M M M M M M M M F F F F F F F F F F Family members 1 2 4 3 4 4 1 2 1 1 1 3 2 3 2 1 1 1 1 2 a) 4pts. Fit a linear regression model using the variables available. Based on the fitted model, would the company prefer male or female customers? Explain. b) 4pts. Would you say that income was an important factor in explaining the variability in profit? Explain. 2. 8pts. A study was done to assess the cost effectiveness of driving a 4-door sedan instead of a van or an SUV (sports utility vehicle). The continuous variables are odometer reading and octane of the gasoline used. The response variable is miles per gallon. The data are presented below: MPG 34.5 33.3 30.4 32.8 35.0 29.0 32.5 29.6 16.8 19.2 Car Type sedan sedan sedan sedan sedan sedan sedan sedan van van Odometer 75000 60000 88000 15000 25000 35000 102000 98000 56000 72000 Octane 87.5 87.5 78.0 78.0 90.0 78.0 90.0 87.5 87.5 90.0 1 22.6 24.4 20.7 25.1 18.8 15.8 17.4 15.6 17.3 20.8 22.2 16.5 21.3 20.7 24.1 van van van van van van van SUV SUV SUV SUV SUV SUV SUV SUV 14500 22000 66500 35000 97500 65500 42000 65000 55500 26500 11500 38000 77500 19500 87000 87.5 90.0 78.0 90.0 87.5 78.0 78.0 78.0 87.5 87.5 90.0 78.0 90.0 78.0 90.0 (a) 2pts.Write the model equation for this problem. (b) 2pts.Add dummy variables to the table for modeling Car Type. (c) 2pts. Write the least-squares prediction equation and provide the interpretation of the partial coefficient estimates. (d) 2pts. Discuss your findings. 2