Question

Dear Expert

I need your perception and answers how to solve this problem

Pagliaci Pizza is developing a new frozen pizza product, and it asked a random sample of 30 customers to rate the product quality (x variable). The company also observed whether the customer bought the product at the end (y variable)

Customer	Quality Rating	Buy or Not (Buy=1, Not buy=0)
1	16	0
2	20	0
3	27	0
4	29	0
5	38	0
6	46	0
7	46	0
8	47	1
9	49	0
10	50	0
11	52	0
12	53	1
13	55	0
14	59	1
15	64	0
16	68	1
17	72	0
18	74	1
19	76	0
20	80	1
21	82	1
22	85	1
23	87	0
24	88	1
25	88	1
26	89	1
27	90	0
28	91	1
29	94	1
30	96	1

a. Write the estimated logistic regression equation relating x to y.

b. Based on the equation in part A), estimate the probability that a customer who gives a score of 90 points will buy the product.

c. Based on the equation in part A), a customer will have a 0.80 or higher probability of buying, what is the value of this score?

Answer 1

16 cases have Y=0; 14 cases have Y=1.

Variable Avg SD   
1 63.7000 23.2496

Iteration History...
-2 Log Likelihood = 41.4554 (Null Model)
-2 Log Likelihood = 39.5305
-2 Log Likelihood = 36.5408
-2 Log Likelihood = 33.6427
-2 Log Likelihood = 31.5231
-2 Log Likelihood = 30.3205
-2 Log Likelihood = 29.8251
-2 Log Likelihood = 29.6966
-2 Log Likelihood = 29.6795
-2 Log Likelihood = 29.6786
-2 Log Likelihood = 29.6786
-2 Log Likelihood = 29.6786 (Converged)

Overall Model Fit...
Chi Square= 11.7768; df=1; p= 0.0006

Coefficients, Standard Errors, Odds Ratios, and 95% Confidence Limits...
Variable Coeff. StdErr p O.R. Low -- High
1 0.0687 0.0248 0.0056 1.0711 1.0203 1.1244
Intercept -4.6551 1.7431 0.0076

Predicted Probability of Outcome, with 95% Confidence Limits...
X Y Prob Low -- High
16.0000 0 0.0278 0.0020 0.2926
20.0000 0 0.0362 0.0031 0.3121
27.0000 0 0.0573 0.0068 0.3489
29.0000 0 0.0652 0.0086 0.3601
38.0000 0 0.1145 0.0230 0.4152
46.0000 0 0.1830 0.0530 0.4726
46.0000 0 0.1830 0.0530 0.4726
47.0000 1 0.1935 0.0586 0.4806
49.0000 0 0.2159 0.0712 0.4970
50.0000 0 0.2277 0.0784 0.5056
52.0000 0 0.2528 0.0944 0.5234
53.0000 1 0.2660 0.1032 0.5328
55.0000 0 0.2936 0.1229 0.5523
59.0000 1 0.3536 0.1691 0.5952
64.0000 0 0.4354 0.2370 0.6569
68.0000 1 0.5037 0.2943 0.7119
72.0000 0 0.5719 0.3494 0.7688
74.0000 1 0.6052 0.3750 0.7965
76.0000 0 0.6375 0.3993 0.8231
80.0000 1 0.6983 0.4434 0.8705
82.0000 1 0.7264 0.4634 0.8909
85.0000 1 0.7654 0.4912 0.9168
87.0000 0 0.7892 0.5085 0.9312
88.0000 1 0.8004 0.5168 0.9376
88.0000 1 0.8004 0.5168 0.9376
89.0000 1 0.8111 0.5249 0.9435
90.0000 0 0.8214 0.5327 0.9489
91.0000 1 0.8313 0.5404 0.9538
94.0000 1 0.8582 0.5625 0.9661
96.0000 1 0.8741 0.5764 0.9726

b) There is a 0.82 probability that a customer who gives a score of 90 points will buy the product.

c) The score is 88 for a 0.80 or higher probability of buying,