A study was done to determine whether the gender of the

Question

1. 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	Family members
157	45000	M	1
-181	55000	M	2
-253	45800	M	4
158	38000	M	3
75	75000	M	4
202	99750	M	4
-451	28000	M	1
146	39000	M	2
89	54350	M	1
-357	32500	M	1
522	36750	F	1
78	42500	F	3
5	34250	F	2
-177	36750	F	3
123	24500	F	2
251	27500	F	1
-56	18000	F	1
453	24500	F	1
288	88750	F	1
-104	19750	F	2

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

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

2. 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	Car Type	Odometer	Octane
34.5	sedan	75000	87.5
33.3	sedan	60000	87.5
30.4	sedan	88000	78.0
32.8	sedan	15000	78.0
35.0	sedan	25000	90.0
29.0	sedan	35000	78.0
32.5	sedan	102000	90.0
29.6	sedan	98000	87.5
16.8	van	56000	87.5
19.2	van	72000	90.0
22.6	van	14500	87.5
24.4	van	22000	90.0
20.7	van	66500	78.0
25.1	van	35000	90.0
18.8	van	97500	87.5
15.8	van	65500	78.0
17.4	van	42000	78.0
15.6	SUV	65000	78.0
17.3	SUV	55500	87.5
20.8	SUV	26500	87.5
22.2	SUV	11500	90.0
16.5	SUV	38000	78.0
21.3	SUV	77500	90.0
20.7	SUV	19500	78.0
24.1	SUV	87000	90.0

(a) Write the model equation for this problem.

(b) Add dummy variables to the table for modeling Car Type. 

(c) Write the least-squares prediction equation and provide the interpretation of the partial coefficient estimates.

(d) Discuss your findings.