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.