Number of family members

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Reference no: EM13855608

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. 

Reference no: EM13855608

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