A bank is interested in identifying different attributes of its customers and below is the sample data

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Question:

A bank is interested in identifying different attributes of its customers and below is the sample data of 150 customers. In the data table for the dummy variable Gender, 0 represents Male and 1 represents Female. And for the dummy variable Personal loan, 0 represents a customer who has not taken personal loan and 1 represents a customer who has taken personal loan.Partition the data into training (50 percent), validation (30 percent), and test (20 percent) sets. Use logistic regression to classify observations as Personal loan taken (or not taken) using Age, Gender, Work experience, Income (in 1000 $), and Family size as input variables and Personal loan as the output variable. Perform an exhaustive-search best subset selection with the number of best subsets equal to 2.

a. From the generated set of logistic regression models, select one that you believe is a good fit. Express the model as a mathematical equation relating the output variable to the input variables.
b. Increases in which variables increase the chance of a customer who has taken the personal loan? Increases in which variables decrease the chance of a customer who has not taken the personal loan?
c. Using the default cutoff value of 0.5 for your logistic regression model, what is the overall error rate on the test data?

Age	Gender	Work experience	Income (in 1000 $)	Family size	Personal loan
47	0	22	53	3	1
26	1	3	22	1	1
38	0	16	29	4	1
37	0	12	32	6	1
44	0	22	32	3	0
55	1	30	45	7	0
44	1	23	50	2	0
30	1	5	22	2	0
63	0	35	56	2	0
34	1	8	23	4	0
52	0	26	29	1	1
55	0	25	34	2	1
52	0	28	45	3	1
63	1	29	23	3	1
51	1	30	32	4	0
41	0	18	21	5	1
37	0	14	43	4	1
46	0	23	23	3	1
30	1	6	18	3	1
48	1	25	34	2	0
50	1	22	21	1	1
56	0	31	24	4	0
35	1	9	23	3	1
39	0	13	29	5	1
48	0	22	34	6	0
51	1	21	39	2	1
27	1	3	26	1	1
57	1	32	49	2	1
33	1	12	39	3	1
58	0	33	32	2	0
46	0	21	45	3	1
32	0	6	23	5	0
56	1	28	45	3	1
35	1	12	28	4	1
47	1	23	38	1	1
50	0	23	32	3	0
57	1	25	32	4	1
38	0	15	25	5	1
52	1	24	22	2	1
56	0	31	19	3	1
47	1	24	34	4	0
54	0	31	45	2	1
25	0	2	21	1	1
40	1	16	34	6	0
61	1	30	49	2	1
29	1	6	34	1	1
52	0	25	39	3	1
56	0	31	54	2	1
61	0	33	43	2	0
26	0	4	23	2	1
60	1	30	56	3	0
37	1	12	23	5	0
39	1	14	39	4	0
46	1	21	34	5	0
59	1	30	39	2	0
54	0	31	28	1	1
27	0	4	22	1	1
54	0	30	45	2	0
42	1	18	36	4	0
64	0	35	46	2	0
33	1	8	32	6	1
65	0	34	36	1	0
38	0	13	32	4	0
48	1	23	26	5	0
31	1	7	32	3	0
39	0	15	35	5	1
58	1	28	45	2	0
51	0	26	23	3	0
41	0	18	34	3	0
36	1	12	32	2	0
39	0	12	22	4	0
58	0	29	34	2	0
42	1	15	45	1	0
44	1	21	32	3	0
65	1	35	54	2	0
40	0	13	23	5	0
33	1	11	41	4	0
45	1	24	29	5	0
38	0	12	24	4	1
32	1	10	28	3	1
51	0	30	43	2	1
32	0	11	34	1	1
46	0	22	39	4	1
44	1	21	25	3	0
41	1	15	28	2	1
54	1	29	54	4	1
26	1	3	24	2	0
33	0	8	26	3	1
45	1	20	34	4	0
63	1	30	54	2	0
55	0	31	49	3	1
49	1	25	34	5	1
64	1	35	54	2	0
26	0	3	19	1	0
42	1	19	23	1	1
48	1	22	43	3	1
64	1	34	45	2	0
52	0	28	32	4	0
41	0	16	34	3	1
40	0	14	34	5	0
40	0	16	26	4	0
55	1	32	37	2	1
49	0	27	39	3	0
46	0	21	29	1	0
59	1	32	56	2	0
51	0	26	23	3	1
45	0	23	43	4	1
39	1	17	26	4	1
55	1	32	37	5	1
63	0	35	43	2	0
53	1	27	24	1	1
39	0	16	43	6	1
50	1	25	56	3	0
27	0	4	32	1	1
29	0	6	23	2	1
61	0	30	45	1	0
57	1	27	34	2	1
56	1	34	54	4	0
35	1	6	45	5	0
25	0	3	32	2	1
57	0	27	36	2	0
47	0	25	54	4	1
60	1	35	33	3	0
32	0	8	45	2	1
27	1	4	32	1	0
39	0	18	39	4	1
26	0	1	22	1	0
46	1	25	34	5	0
28	0	4	23	2	0
64	0	37	43	4	0
65	1	33	49	2	0
47	1	25	37	4	0
27	1	5	28	2	1
25	0	3	34	1	1
25	0	2	24	1	1
64	0	30	53	2	0
44	1	21	48	5	1
65	0	25	47	2	0
54	0	31	55	1	1
51	0	26	43	3	0
51	0	21	46	1	1
28	1	4	25	2	1
56	1	32	55	3	1
57	1	26	49	2	1
35	1	9	27	6	1
47	1	21	54	4	1
54	1	27	45	2	0
28	1	5	29	3	1
45	0	22	45	5	0
43	1	18	43	2	1