Suppose a bank would like to develop a regression model to predict a? person\'s
ID: 3367792 • 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
592 1,383 55 Bachelor Own
702 1,707 65 Bachelor Rent
663 801 44 High School Own
634 694 42 Bachelor Own
595 1,156 35 High School Rent
598 1,555 38 Graduate Rent
673 895 25 Graduate Own
610 1,246 40 Bachelor Own
754 1,076 33 Bachelor Own
620 1,554 41 High School Own
690 719 42 Bachelor Own
573 558 41 Bachelor Rent
699 1,227 35 Bachelor Own
651 1,343 44 Bachelor Own
807 1,400 52 Graduate Own
599 1,273 51 High School Rent
735 1,513 55 Bachelor Own
698 1,801 52 High School Own
696 1,163 51 Bachelor Rent
739 1,294 41 Bachelor Own
671 1,404 50 Bachelor Rent
694 1,879 49 Bachelor Own
580 762 33 High School Own
682 1,154 34 Bachelor Own
617 1,121 45 High School Rent
675 992 45 Bachelor Rent
621 615 33 Bachelor Rent
556 1,087 34 High School Own
621 1,177 57 High School Own
681 1,813 46 High School Own
536 1,019 28 High School Rent
635 1,380 38 High School Own
621 1,852 33 Bachelor Rent
642 1,090 49 Bachelor Own
635 777 55 Bachelor Own
657 921 43 Bachelor Rent
784 1,435 60 Bachelor Own
718 1,577 54 High School Own
639 913 52 Bachelor Rent
687 1,097 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,
x 1x=Income?,
x2=Age,
x3=Ed 1,
x4=Ed2?,
and
x5=Res
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. Select the correct choice below and fill in the answer boxes to complete your choice.
?(Round to the nearest integer as? needed.)??
A.
Bachelor degree holders average credit scores that are _ points higher than people with only a high school degree.
Graduate degree holders average credit scores that are _ points higher than people with only a high school degree.
People who own their primary residence average credit scores that are _ points higher than renters.
B.
Bachelor degree holders average credit scores that are _ points higher than people with only a high school degree.
Graduate degree holders average credit scores that are _ points higher than people with only a bachelor degree.
People who rent their primary residence average credit scores that are _ points higher than owners.
c. A test for the significance of the overall regression model shows that it is significant using
alpha =.05
Using the? p-values, identify which independent variables are significant with .05
A.Ed 1
B.Ed 2
C.Res
D.Age
E.Income
D. Construct a regression model using only the significant variables found in part c and predict the average credit score for a 40?-year-old
person who earns 1,200 per? month, has a
graduate degree, and owns his or her residence.
The predicted average credit score is
Explanation / Answer
Following is the data set with dummy variables:
Following is the output of regression analysis:
The required model is:
y' = 466.36+0.04*x1 +1.95*x2+46.81*x3+81.04*x4+41.00*x5
B.
Bachelor degree holders average credit scores that are 46.81 points higher than people with only a high school degree.
Graduate degree holders average credit scores that are 81.04 points higher than people with only a bachelor degree.
People who rent their primary residence average credit scores that are 41.00 points higher than owners.
(c)
P-value of income(x1) is greater than 0.05 so it is not signficant to the model. Rest all are signficant to the model.
(d)
The required predicted score is:
y' = 466.36+0.04*1200 +1.95*40+46.81*0+81.04*1+41.00*1=714.4
The predicted average credit score is: 714.4
Credit_Score Income_($), X1 Age, X2 Ed1, X3 Ed2, X4 Res, X5 592 1383 55 1 0 1 702 1707 65 1 0 0 663 801 44 0 0 1 634 694 42 1 0 1 595 1156 35 0 0 0 598 1555 38 0 1 0 673 895 25 0 1 1 610 1246 40 1 0 1 754 1076 33 1 0 1 620 1554 41 0 0 1 690 719 42 1 0 1 573 558 41 1 0 0 699 1227 35 1 0 1 651 1343 44 1 0 1 807 1400 52 0 1 1 599 1273 51 0 0 0 735 1513 55 1 0 1 698 1801 52 0 0 1 696 1163 51 1 0 0 739 1294 41 1 0 1 671 1404 50 1 0 0 694 1879 49 1 0 1 580 762 33 0 0 1 682 1154 34 1 0 1 617 1121 45 0 0 0 675 992 45 1 0 0 621 615 33 1 0 0 556 1087 34 0 0 1 621 1177 57 0 0 1 681 1813 46 0 0 1 536 1019 28 0 0 0 635 1380 38 0 0 1 621 1852 33 1 0 0 642 1090 49 1 0 1 635 777 55 1 0 1 657 921 43 1 0 0 784 1435 60 1 0 1 718 1577 54 0 0 1 639 913 52 1 0 0 687 1097 46 0 1 0Related Questions
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