Question

The file P17_05.xlsx contains data on 100 consumers who drink beer. Some of them prefer light beer, and others prefer regular beer. A major beer producer believes that the following variables might be useful in discriminating between these two groups: gender, marital status, annual income level, and age. b. Consider a new customer: male, married, income $42,000, age 47. Use the logistic regression equation to estimate the probability that this customer prefers Regular. How would you classify this person?

Individual	Gender	Married	Income	Age	Beer Preference
1	1	0	$37,779	45	Regular
2	0	1	$44,955	53	Regular
3	1	0	$36,896	48	Regular
4	1	1	$70,981	45	Light
5	1	0	$38,990	36	Regular
6	1	1	$51,126	41	Light
7	0	1	$45,133	51	Light
8	1	1	$36,316	41	Light
9	1	1	$40,955	69	Regular
10	0	1	$27,280	55	Regular
11	0	1	$33,027	51	Regular
12	1	1	$63,555	62	Light
13	1	1	$64,709	70	Regular
14	1	0	$38,447	37	Light
15	1	1	$35,282	59	Regular
16	0	1	$43,468	52	Regular
17	1	0	$53,768	34	Light
18	0	1	$52,875	71	Light
19	1	0	$29,728	41	Regular
20	0	0	$30,587	36	Regular
21	0	1	$49,585	34	Light
22	1	1	$48,957	33	Light
23	1	1	$32,739	50	Regular
24	1	0	$41,057	40	Light
25	1	0	$31,916	43	Regular
26	1	0	$29,077	39	Regular
27	1	1	$58,164	30	Light
28	0	1	$30,784	52	Regular
29	1	1	$25,440	51	Regular
30	0	0	$41,779	39	Light
31	0	0	$26,598	29	Light
32	1	1	$30,081	56	Regular
33	1	1	$43,194	47	Light
34	1	0	$22,408	40	Regular
35	1	1	$42,108	26	Light
36	0	0	$40,456	42	Light
37	1	1	$47,797	49	Light
38	1	0	$43,992	53	Light
39	1	1	$41,882	54	Regular
40	1	1	$55,281	48	Light
41	1	1	$47,495	35	Light
42	0	0	$33,088	22	Light
43	0	1	$46,890	36	Light
44	0	0	$35,406	29	Light
45	0	1	$59,485	36	Light
46	1	0	$42,775	27	Light
47	0	0	$28,094	39	Regular
48	1	0	$26,004	62	Regular
49	1	0	$38,671	44	Light
50	0	1	$33,880	48	Regular
51	0	0	$43,593	27	Light
52	0	0	$27,078	45	Regular
53	1	0	$37,926	33	Light
54	1	1	$50,517	38	Light
55	0	0	$39,370	28	Light
56	0	0	$31,398	47	Regular
57	1	0	$29,293	43	Regular
58	1	0	$49,811	49	Regular
59	0	0	$38,453	43	Regular
60	0	0	$31,779	46	Regular
61	0	1	$33,700	25	Light
62	0	1	$37,263	49	Regular
63	0	1	$44,802	34	Light
64	0	1	$35,050	36	Light
65	1	1	$37,606	37	Light
66	1	0	$52,341	42	Light
67	1	1	$45,600	50	Regular
68	1	1	$36,030	55	Regular
69	0	1	$44,558	31	Light
70	1	1	$34,391	60	Regular
71	1	1	$43,741	54	Regular
72	0	0	$36,821	32	Light
73	1	1	$51,578	45	Light
74	1	0	$23,234	31	Regular
75	0	1	$48,259	32	Light
76	0	1	$46,273	56	Light
77	1	1	$42,404	30	Light
78	0	0	$41,391	54	Light
79	0	1	$45,610	38	Light
80	1	1	$47,667	87	Regular
81	1	1	$40,261	31	Light
82	1	0	$46,626	46	Light
83	0	1	$55,608	43	Light
84	1	1	$35,678	64	Regular
85	0	0	$50,154	40	Light
86	1	0	$34,575	57	Regular
87	0	0	$30,841	24	Light
88	1	0	$20,945	42	Regular
89	1	0	$38,176	40	Regular
90	1	0	$28,513	34	Regular
91	0	1	$51,094	46	Regular
92	1	1	$40,582	66	Regular
93	1	0	$32,493	63	Regular
94	0	1	$36,451	44	Regular
95	0	1	$42,051	58	Regular
96	0	0	$26,186	38	Regular
97	1	1	$24,302	46	Regular
98	0	0	$39,923	58	Regular
99	0	1	$39,942	21	Light
100	1	0	$33,553	48	Regular

Answer 1

a) I have performed the logistic regression in R. Here is the code:

R Code:

beer<-read.csv("beer.csv")
logitmod<-glm(Beer.Preference~Gender + Married + Income + Age, family="binomial",data = beer)
summary(logitmod)

Output:

Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 6.819e-01 1.931e+00 0.353 0.724
Gender 7.779e-01 7.166e-01 1.085 0.278
Married -1.697e-01 7.945e-01 -0.214 0.831
Income -2.785e-04 6.334e-05 -4.396 1.10e-05 ***

B) For prediction, R Code:

person<-data.frame(Gender=1,Married=1,Income=42000,Age=45)
predict(logitmod,person,type="response")

Output: 0.466

As the output is the probability to predict the probability of Event '1' = 'Regular'. Hence, as p-value<0.5, we can say that the person prefers Light beer.