Dear Expert I need your perception and answers how to solve this problem Pagliac

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)

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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?

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

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Explanation / Answer

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,

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