Use the data below and R studio to answer the questions:

1. The dependent variable is coded as y=1 if the customer used a coupon and 0 if not. Suppose that the only information available to help predict whether the customer will use the coupon is the credit card status, coded as x=1, if the customer has the store's credit card and x=0 if not. a.Is the use of a coupon independent of the card status?
   1. Fit the logistic regression model to predict the chances of a customer to use the coupon using as independent variable the card status. Paste the summary of the model in your report.
   2. Use the estimated logistic regression to calculate the probability that a customer who does not have the stores credit card uses the coupon.
   3. Use the estimated logistic regression to calculate the probability that a customer who has the store's credit card uses the coupon.
   4. Compare the estimated probabilities in question 2 and 3. What can you conclude about the effect of credit card status on the chances of a customer to use the coupon.
2. Fit a logistic regression to predict the chances of a customer to use a coupon using as independent variables their annual spending and the credit card status. a.State the estimated logistic regression
   1. Use the estimated logistic regression to estimate the probability that a customer with an annual spending of $4000 who has the store's credit uses the coupon.
   2. Use the estimated logistic regression to estimate the probability that a customer with an annual spending of $5000 who has the store's credit uses the coupon.
   3. Compare the estimated probability calculated in questions b and c. What can you conclude about the effect of the annual spending on the chances of a customer to use the coupon?
   4. Use the estimated equation and a threshold of 50% to calculate the true positive rate and the false positive rate. Comment on the performance of the model at this threshold.
   5. Calculate the AUC and comment on the general performance of this model.

Customer	Spending	Card	Coupon
1	2.291	1	0
2	3.215	1	0
3	2.135	1	0
4	3.924	0	0
5	2.528	1	0
6	2.473	0	1
7	2.384	0	0
8	7.076	0	0
9	1.182	1	1
10	3.345	0	0
11	2.14	1	0
12	3.255	0	1
13	1.512	0	0
14	2.148	0	1
15	6.737	0	0
16	6.486	0	0
17	1.307	0	0
18	3.47	1	0
19	2.936	0	0
20	6.404	0	1
21	2.229	0	0
22	2.933	0	0
23	2.118	0	0
24	2.05	0	0
25	4.998	0	1
26	1.394	0	0
27	3.993	1	1
28	2.059	0	1
29	1.677	0	0
30	2.229	0	1
31	1.138	0	0
32	2.933	1	0
33	5.365	1	1
34	5.365	0	0
35	6.179	0	0
36	1.98	1	0
37	1.058	1	0
38	6.851	1	1
39	1.124	0	0
40	1.911	0	0
41	3.253	0	0
42	1.839	0	0
43	1.657	1	0
44	1.075	0	0
45	3.566	0	0
46	2.118	0	0
47	1.554	1	0
48	4.631	0	0
49	4.345	1	1
50	4.004	1	1
51	1.068	1	1
52	2.421	0	0
53	4.414	0	0
54	3.386	1	1
55	1.677	1	0
56	2.05	1	1
57	2.323	1	1
58	5.501	0	0
59	3.345	0	1
60	3.318	1	1
61	4.721	0	1
62	1.662	0	1
63	2.936	1	0
64	2.049	0	0
65	2.313	0	1
66	6.851	0	0
67	2.291	0	0
68	3.47	1	1
69	3.253	0	0
70	2.059	0	0
71	2.678	1	1
72	2.323	1	0
73	1.878	1	0
74	2.678	1	1
75	6.179	1	1
76	3.411	1	1
77	5.991	0	1
78	7.076	1	1
79	3.255	1	1
80	2.148	1	0
81	5.501	1	1
82	5.991	1	1
83	2.372	1	0
84	3.995	1	0
85	2.135	0	1
86	6.737	1	1
87	6.486	1	1
88	2.429	1	0
89	4.701	1	1
90	6.404	1	0
91	1.13	1	0
92	1.911	1	1
93	4.959	1	1
94	6.073	1	1
95	1.403	1	0
96	3.318	0	0
97	2.421	1	0
98	6.073	0	0
99	2.63	1	0
100	3.411	0	1