Question

In: Statistics and Probability

Suppose a bank would like to develop a regression model to predict a? person's credit score...

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

Solutions

Expert Solution

Following is the data set with dummy variables:

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 0

Following is the output of regression analysis:

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.681388827
R Square 0.464290733
Adjusted R Square 0.385509958
Standard Error 47.10361157
Observations 40
ANOVA
df SS MS F Significance F
Regression 5 65380.49243 13076.09849 5.893452247 0.000502495
Residual 34 75437.50757 2218.750223
Total 39 140818
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 466.3645044 41.88119073 11.13541655 6.9257E-13 381.251685 551.4773238
Income_($), X1 0.036325064 0.023608211 1.538662324 0.133142576 -0.011652592 0.08430272
Age, X2 1.948262306 0.901226673 2.161789441 0.037763813 0.116749358 3.779775254
Ed1, X3 46.81027664 16.82634082 2.781964133 0.008751731 12.6150381 81.00551519
Ed2, X4 81.04265406 27.18387093 2.98127718 0.005274371 25.79838194 136.2869262
Res, X5 41.00052118 15.59421501 2.629213535 0.012758092 9.309263522 72.69177884

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


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