6.3 Credit Cards

We have a dataset with information on ten thousand customers. The objective is to predict which customers will stop paying their credit card debt.

Fuente: James, G., Witten, D., Hastie, T., and Tibshirani, R. (2013) An Introduction to Statistical Learning with applications in R, www.StatLearning.com, Springer-Verlag, New York

Probabilidad de Impago: Datos
	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
default	No	No	No	No	No	No	No	No	No	No	No	No	No	No	No	No	No	No	No	No
balance	729.53	817.18	1073.55	529.25	785.66	919.59	825.51	808.67	1161.06	0.00	0.00	1220.58	237.05	606.74	1112.97	286.23	0.00	527.54	485.94	1095.07

	137	174	202	207	210	242	244	264	342	346	350	358	407	440	441	488	541	546	577	582
default	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
balance	1487.00	2205.80	1774.69	1889.60	1899.39	1572.86	1964.48	1530.35	1642.82	1991.65	1550.45	1328.89	1700.60	1118.70	1119.10	1981.45	1717.07	1465.21	1763.58	1770.97

	9981	9982	9983	9984	9985	9986	9987	9988	9989	9990	9991	9992	9993	9994	9995	9996	9997	9998	9999	10000
default	No	No	No	No	No	No	No	No	No	No	No	No	No	No	No	No	No	No	No	No
balance	770.02	739.42	623.53	506.63	875.24	842.95	401.33	1092.91	0.00	999.28	372.38	658.80	1111.65	938.84	172.41	711.56	757.96	845.41	1569.01	200.92

Probabilidad de Impago: Resumen de Datos
No	Variable	Stats / Values	Freqs (% of Valid)	Graph	Missing
1	default [numeric]	Min : 0 Mean : 0 Max : 1	0 : 9667 (96.7%) 1 : 333 ( 3.3%)		0 (0.0%)
2	balance [numeric]	Mean (sd) : 835.4 (483.7) min < med < max: 0 < 823.6 < 2654.3 IQR (CV) : 684.6 (0.6)	9227 distinct values		0 (0.0%)

Using simple Linear Regression

Using Logistic Regression

\[ \log\left[ \frac { \widehat{P( \operatorname{default} = \operatorname{1} )} }{ 1 - \widehat{P( \operatorname{default} = \operatorname{1} )} } \right] = -10.65 + 0.01(\operatorname{balance}) \]

Observations	10000
Dependent variable	default
Type	Generalized linear model
Family	binomial
Link	logit

χ²(1)	1324.198
Pseudo-R² (Cragg-Uhler)	0.490
Pseudo-R² (McFadden)	0.453
AIC	1600.451
BIC	1614.872

	Est.	S.E.	z val.	p
(Intercept)	-10.651	0.361	-29.492	0.000
balance	0.005	0.000	24.953	0.000
Standard errors: MLE

Exercise

Interpret the estimated coefficients
Is this a good model?