Question

MRE2. The file Credit Approval Decisions Coded provides information on credit history for a sample of banking customers. (18 pts)

a.         Use regression analysis to identify the best model to predict credit score based on the other             variables.

b.         Report and interpret R² and Standard Error (SE) for the model developed in a.

c.         Interpret the regression coefficient(s) for the model developed in a.

DATA:

Coded Credit Approval Decisions
Homeowner	Credit Score	Years of Credit History	Revolving Balance	Revolving Utilization	Decision
1	725	20	$             11,320	25%	1
1	573	9	$               7,200	70%	0
1	677	11	$             20,000	55%	1
0	625	15	$             12,800	65%	0
0	527	12	$               5,700	75%	0
1	795	22	$               9,000	12%	1
0	733	7	$             35,200	20%	1
0	620	5	$             22,800	62%	0
1	591	17	$             16,500	50%	0
1	660	24	$               9,200	35%	1
1	700	19	$             22,000	18%	1
1	500	16	$             12,500	83%	0
1	565	6	$               7,700	70%	0
0	620	3	$             37,400	87%	0
1	774	13	$               6,100	7%	1
1	802	10	$             10,500	5%	1
0	640	7	$             17,300	59%	0
0	523	14	$             27,000	79%	0
1	811	20	$             13,400	3%	1
0	763	2	$             11,200	70%	0
0	555	4	$               2,500	100%	0
0	617	9	$               8,400	34%	0
1	642	13	$             16,000	25%	1
0	688	3	$               3,300	11%	1
1	649	12	$               7,500	5%	1
1	695	15	$             20,300	22%	1
1	701	9	$             11,700	15%	1
0	635	7	$             29,100	85%	0
0	507	2	$               2,000	100%	0
1	677	12	$               7,600	9%	1
0	485	5	$               1,000	80%	0
0	582	3	$               8,500	65%	0
1	699	17	$             12,800	27%	1
1	703	22	$             10,000	20%	1
0	585	18	$             31,000	78%	0
1	620	8	$             16,200	55%	0
1	695	16	$               9,700	11%	1
1	774	13	$               6,100	7%	1
1	802	10	$             10,500	5%	1
0	640	7	$             17,300	59%	0
0	536	14	$             27,000	79%	0
1	801	20	$             13,400	3%	1
0	760	2	$             11,200	70%	0
0	567	4	$               2,200	95%	0
0	600	10	$             12,050	81%	0
1	702	11	$             11,700	15%	1
1	636	8	$             29,100	85%	0
0	509	3	$               2,000	100%	0
0	595	18	$             29,000	78%	0
1	733	15	$             13,000	24%	1

Answer 1

A-

Regression Analysis - Best Model (Y - Credit score X - Revolving Utilization )

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.796420254
R Square	0.63428522
Adjusted R Square	0.626666162
Standard Error	55.00605103
Observations	50
ANOVA
	df	SS	MS	F	Significance F
Regression	1	251886.1288	251886.1288	83.2498	0.0000
Residual	48	145231.9512	3025.6656
Total	49	397118.0800
	Coefficients	Standard Error	t Stat	P-value
Intercept	757.9223	13.9489	54.3357	0.0000
Revolving Utilization	-220.7319	24.1921	-9.1241	0.0000

So Model Will be, Credit Score = 757.9223 - 220.7319 * Revolving Utilization

B - R Square - 0.63428522 or 63.428522%

Standard Error - 55.00605103

Interpretation

R square - 63.428533% change in Credit Score is explained by revolving utilization

Standard Error - The Standard error of 55.00605103 indicates the variability of predicted values from actual ones.

C.

Anova / F stat

Null Hypothesis - Credit Score is not dependent on the Independent Variables (i.e. Homeowner, Revolving Utilization, Revolving Balance, Years of credit history and decision)

Alternate Hypothesis - Credit Score is dependent on all or any of the Independent Variables (i.e. Homeowner, Revolving Utilization, Revolving Balance, Years of credit history and decision)

If P value of F stat > 0.05 - We Cannot Reject the Null Hypothesis

If P value of F stat < 0.05 - We Can Reject the Null Hypothesis

Since the P value of F stat is 0.0000, which is less than 0.05, so can reject the null hypothesis, Meaning that we should accept the alternate hypothesis. So we can say that Credit Score is dependent on all or any of the Independent Variables (i.e. Homeowner, Revolving Utilization, Revolving Balance, Years of credit history and decision).

Model is Significant

T stat

Null Hypothesis - Credit Score is not dependent on revolving utilization

Alternate Hypothesis - Credit Score is dependent on revolving utilization.

If P value of T stat > 0.05 - We Cannot Reject the Null Hypothesis

If P value of T stat < 0.05 - We Can Reject the Null Hypothesis

Since the P value of T stat is 0.0000, which is less than 0.05, so can reject the null hypothesis, Meaning that we should accept the alternate hypothesis. So we can say that Credit Score is dependent on revolving Utilization.

There is a 0% chance that the coefficient of revolving utilization is 0.

Revolving utilization is a significant variable for credit score