Suppose a bank would like to develop a regression model to predict a person\'s c
ID: 3360596 • Letter: S
Question
Suppose a bank would like to develop a regression model to predict a person's credit score based on his or her age, weekly income, highest education level (high school, bachelor degree, graduate degree), and whether or not he or she owns or rents his or her primary residence. The accompanying table provides these data for a random sample of customers. Complete parts a through d below.
Credit Score
Income
Age
Education
Residence
($)
593
1,404
57
Bachelor
Own
705
1,697
64
Bachelor
Rent
660
800
44
High School
Own
639
682
42
Bachelor
Own
601
1,171
35
High School
Rent
590
1,579
38
Graduate
Rent
679
906
24
Graduate
Own
611
1,257
41
Bachelor
Own
750
1,092
35
Bachelor
Own
629
1,574
42
High School
Own
691
700
42
Bachelor
Own
571
522
40
Bachelor
Rent
699
1,206
34
Bachelor
Own
648
1,323
43
Bachelor
Own
812
1,378
53
Graduate
Own
599
1,272
50
High School
Rent
733
1,503
55
Bachelor
Own
707
1,806
52
High School
Own
694
1,163
51
Bachelor
Rent
737
1,305
40
Bachelor
Own
678
1,401
51
Bachelor
Rent
695
1,870
50
Bachelor
Own
578
800
34
High School
Own
677
1,119
33
Bachelor
Own
615
1,126
45
High Schoo
Rent
677
992
45
Bachelor
Rent
626
624
34
Bachelor
Rent
559
1,057
33
High School
Own
614
1,196
58
High School
Own
679
1,810
45
High School
Own
531
1,051
30
High School
Rent
631
1,367
38
High School
Own
620
1,855
35
Bachelor
Rent
644
1,090
50
Bachelor
Own
635
775
55
Bachelor
Own
660
905
43
Bachelor
Rent
781
1,416
59
Bachelor
Own
718
1,577
54
High School
Own
645
908
52
Bachelor
Rent
685
1,087
46
Graduate
Rent
a. Using technology, construct a regression model using all of the independent variables. (Let variable Ed1 be one of the dummy variables for the education level. Assign a 1 to a bachelor degree for this variable. Let Ed2 be another dummy variable for the education level. Assign a 1 to a graduate degree for this variable. Also, let variable Res be the dummy variable for the Residence variable. Assign a 1 if the person owns his or her primary residence.)Complete the regression equation for the model below, where
y=Credit Score,
x1=Income,
x2=Age,
x3=Ed1,
x4=Ed2, and
x5=Res.
ModifyingAbove y= ____ + ( )x1 + ( ) x2 + ( ) x3 + ( ) x4 + ( ) x5
(Round to two decimal places as needed.)
b. Interpret the meaning of each of the regression coefficients for the dummy variables.
c. A test for the significance of the overall regression model shows that it is significant using =0.05. Using the p-values, identify which independent variables are significant with =0.05.
d. Construct a regression model using only the significant variables found in part c and predict the average credit score for a 33-year-old person who earns 1,550 per month, has a bachelor
degree, and owns his or her residence.
Credit Score
Income
Age
Education
Residence
($)
593
1,404
57
Bachelor
Own
705
1,697
64
Bachelor
Rent
660
800
44
High School
Own
639
682
42
Bachelor
Own
601
1,171
35
High School
Rent
590
1,579
38
Graduate
Rent
679
906
24
Graduate
Own
611
1,257
41
Bachelor
Own
750
1,092
35
Bachelor
Own
629
1,574
42
High School
Own
691
700
42
Bachelor
Own
571
522
40
Bachelor
Rent
699
1,206
34
Bachelor
Own
648
1,323
43
Bachelor
Own
812
1,378
53
Graduate
Own
599
1,272
50
High School
Rent
733
1,503
55
Bachelor
Own
707
1,806
52
High School
Own
694
1,163
51
Bachelor
Rent
737
1,305
40
Bachelor
Own
678
1,401
51
Bachelor
Rent
695
1,870
50
Bachelor
Own
578
800
34
High School
Own
677
1,119
33
Bachelor
Own
615
1,126
45
High Schoo
Rent
677
992
45
Bachelor
Rent
626
624
34
Bachelor
Rent
559
1,057
33
High School
Own
614
1,196
58
High School
Own
679
1,810
45
High School
Own
531
1,051
30
High School
Rent
631
1,367
38
High School
Own
620
1,855
35
Bachelor
Rent
644
1,090
50
Bachelor
Own
635
775
55
Bachelor
Own
660
905
43
Bachelor
Rent
781
1,416
59
Bachelor
Own
718
1,577
54
High School
Own
645
908
52
Bachelor
Rent
685
1,087
46
Graduate
Rent
Explanation / Answer
Credit Score = 469 + 0.0349 Income + 1.91 Age + 47.6 Ed1 + 81.5 Ed2+ 41.0 Residence
Source DF SS MS F P-Value
Regression 5 63909 12782 5.54 0.001
Residual Error 34 78503 2309
Total 39 142412
The variable which shows significant value at 0.05 significant value are age, Ed1, Ed2 & Residence.
Predictor Coef SE.Coef T .Test P-Value
Constant 469.37 43.05 10.90 0.000
Income 0.03495 0.02409 1.45 0.156
Age 1.9099 0.9284 2.06 0.047
Ed1 47.60 17.24 2.76 0.009
Ed2 81.49 27.74 2.94 0.006
Residence 41.03 15.90 2.58 0.014
Credit Score = 490 + 2.42 Age + 42.6 Ed1 + 82.0 Ed2 + 43.5 Residence excluding Income variable as it was not significant.
Credit Score(1,550 )= 490 + 2.42 *(33) + 42.6 *(1) + 82.0 *(0) + 43.5*(1) = 655.96
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