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Perform a logit and probit analysis of the variables that affect whether a customer takes out a loan. Consider only main effects. Which variables are significant? How do the significant variables influence the likelihood of taking out a loan? Copy screen snapshots of your analysis in R to your report. (20%)

Answer –

Selected the attributes not in red as the ones that are meaningful, as impacting someone getting a personal loan. Personal Loan is the resulting value.

Legends –

Variables in bold are significant

Color notation

	intutive
	non intutive
0	no loan
1	loan

logit :
Coefficients:
	Estimate	Std. Error	z value	Pr(>\|z\|)
(Intercept)	-9.4198094	0.45714157	-20.606	< 2e-16	***
Age	0.00790014	0.00568947	1.389	0.16497
CCAvg	0.06116208	0.03310581	1.847	0.06468	.
CDAccount	3.25884502	0.26617751	12.243	< 2e-16	*******
CreditCard	-0.9895626	0.18303085	-5.407	6.43E-08	***
Family	0.84227277	0.06983048	12.062	< 2e-16	*******
Income	0.04261172	0.00201485	21.149	< 2e-16	*******
Mortgage	0.00006727	0.00048133	0.14	0.88885
SecuritiesAccount	-0.8324365	0.2534961	-3.284	0.00102	**

variables influence the likelihood of taking out a loan: variables in green and are significant and intutive

probit :

Coefficients:
	Estimate	Std. Error	z value	Pr(>\|z\|)
(Intercept)	-4.9152874	0.22786528	-21.571	< 2e-16	***
Age	0.00349745	0.00299645	1.167	0.24313
CCAvg	0.04330281	0.0181783	2.382	0.017214	*
CDAccount	1.70007706	0.13661644	12.444	< 2e-16	*******
CreditCard	-0.482478	0.09313191	-5.181	2.21E-07	***
Family	0.40058921	0.03538077	11.322	< 2e-16	*******
Income	0.02248318	0.00103494	21.724	< 2e-16	*******
Mortgage	0.00007086	0.00026259	0.27	0.787284
SecuritiesAccount	-0.4296079	0.13052363	-3.291	0.000997	*******

R commander screenshot :

2. Add moderating effects (interactions of variables). Which interactions make sense conceptually? Which interactions are statistically significant? How do you interpret the coefficients on these variables? Copy screen snapshots of your analysis in R to your report. (20%)

Coefficients:
	Estimate	Std. Error	z value	Pr(>\|z\|)
(Intercept)	-3.6146848	0.4796968	-7.535	4.87E-14	***
Family	-1.4895358	0.2119153	-7.029	2.08E-12	***
Income	0.0001998	0.0038434	0.052	0.959
Family:Income	0.0202891	0.0018521	10.955	< 2e-16	***

The moderating effects coefficient is positive , which means it has an accelerating impact.

	definition	input	output
(Intercept)	always1	1	-3.6146848
Family	number of family members	4	-5.9581432
Income	income in 1000 $	200	0.03996
Family:Income	moderating effect	800	16.23128
	sum		6.698412
	exp(sum)		811.116749
probability	exp(sum)/(1+exp(sum))	100%

3. Create a final regression model with the variables that you feel are important (both main effects and interaction terms). Create a spreadsheet prediction of the model. Which variables have the greatest influence on the customers’ loan behavior (combined main effects and interaction effects)? Perform a sensitivity analysis as seen earlier in the semester. Copy screen snapshots of your analysis in R to your report. (20%)

Logit

Coefficients	:
	Estimate	Std. Error	z value	Pr(>\|z\|)
(Intercept)	-9.18953	0.3619	-25.393	< 2e-16	***
CDAccount	2.8646	0.22651	12.647	< 2e-16	***
CreditCard	-0.88961	0.17821	-4.992	5.98E-07	***
Family	0.84717	0.06939	12.21	< 2e-16	***
Income	0.04461	0.00179	24.92	< 2e-16	***


	definition	input	output
(Intercept)	always1	1	-9.18953	income
CDAccount	no idea	1	2.8646
CreditCard	number of cards	1	-0.88961
Family	number of family members	4	3.38868
Income	income in 1000 $	200	8.922
	sum		5.09614
	exp(sum)		163.390003
probability	exp(sum)/(1+exp(sum))	99%

sensitivity analysis

	family members
99%	1	2	3	4
10	0%	1%	1%	3%
20	0%	1%	2%	5%
30	1%	2%	3%	8%
40	1%	2%	5%	11%
50	2%	4%	8%	17%
60	2%	6%	12%	24%
70	4%	8%	18%	33%
80	6%	12%	25%	44%
90	9%	18%	34%	55%
100	13%	26%	45%	65%
110	19%	35%	56%	75%
120	27%	46%	66%	82%
130	36%	57%	76%	88%
140	47%	67%	83%	92%
150	58%	76%	88%	95%
160	68%	83%	92%	96%
170	77%	89%	95%	98%
180	84%	92%	97%	99%
190	89%	95%	98%	99%
200	93%	97%	99%	99%
210	95%	98%	99%	100%
220	97%	99%	99%	100%

Probit

Coefficient	s:
	Estimate	Std. Error	z value	Pr(>\|z\|)
(Intercept)	-4.8230308	0.176111	-27.386	< 2e-16	***
CDAccount	1.5112701	0.1178771	12.821	< 2e-16	***
CreditCard	-0.434615	0.0908606	-4.783	0.00000172	***
Family	0.4034737	0.0351834	11.468	< 2e-16	***
Income	0.0238448	0.0009083	26.251	< 2e-16	***


	definition	input	output
(Intercept)	always1	1	-4.8230308
CDAccount	no idea	1	1.5112701
CreditCard	number of cards	1	-0.434615
Family	number of family members	4	1.6138948
Income	income in 1000 $	200	4.76896
	sum		2.6364791

	probability		100%

sensitivity analysis

	family members
100%	1	2	3	4
10	0%	0%	1%	3%
20	0%	1%	2%	5%
30	0%	1%	3%	8%
40	1%	2%	6%	12%
50	2%	4%	9%	17%
60	3%	7%	13%	24%
70	5%	10%	19%	32%
80	8%	15%	26%	41%
90	12%	21%	35%	51%
100	17%	29%	44%	60%
110	24%	38%	53%	69%
120	32%	47%	63%	77%
130	40%	56%	71%	83%
140	50%	65%	79%	89%
150	59%	74%	85%	93%
160	68%	81%	90%	95%
170	76%	87%	94%	97%
180	83%	91%	96%	98%
190	88%	94%	98%	99%
200	92%	97%	99%	100%
210	95%	98%	99%	100%
220	97%	99%	100%	100%

4. Perform a neural network analysis of the variables found to be significant in the logit and probit analysis above. Copy screen snapshots of your final neural network model in R to your report. (20%)

5. Create a prediction model of the neural network. Using the prediction model, perform a sensitivity analysis for the neural network model similar to the logit and probit sensitivity analysis. (20%)