The dating web site Oollama.com requires its users to create profiles based on a survey in which they rate their interest (on a scale from 0 to 3) in five categories: physical fitness, music, spirituality, education, and alcohol consumption. A new Oollama customer, Erin O?Shaughnessy, has reviewed the profiles of 40 prospective dates and classified whether she is interested in learning more about them.

Based on Erin?s classification of these 40 profiles, Oollama has applied a logistic regression to predict Erin?s interest in other profiles that she has not yet viewed. The resulting logistic regression model is as follows:

For the 40 profiles (observations) on which Erin classified her interest, this logistic regression model generates that following probability of Interested.

(a) ?Using a cutoff value of 0.5 to classify a profile observation as Interested or not, construct the confusion matrix for this 40-observation training set. Compute sensitivity, specificity, and precision measures and interpret them within the context of Erin?s dating prospects.

(b) Oollama understands that its clients have a limited amount of time for dating and therefore use decile-wise lift charts to evaluate their classification models. For the training data, what is the first decile lift resulting from the logistic regression model? Interpret this value.

(c) A recently posted profile has values of Fitness = 3, Music = 1, Education = 3, and Alcohol = 1. Use the estimated logistic regression equation to compute the probability of Erin?s interest in this profile.

Observation 35 21 29 25 39 26 23 33 1 24 28 36 16 27 30 32 34 37 40 38 Interested 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 Probability of Interested 1.000 0.999 0.999 0.999 0.999 0.990 0.981 0.974 0.882 0.882 0.882 0.882 0.791 0.791 0.791 0.791 0.791 0.791 0.791 0.732 Observation 13 2 3 7 9 12 18 22 31 6 20 15 5 14 19 8 10 17 4 11 Interested O O O 0 0 0 0 0 0 0 1 1 0 0 0 0 0 OOOOOOO 0 0 0 0 0 Probability of Interested 0.412 0.285 0.219 0.168 0.168 0.168 0.168 0.168 0.168 0.128 0.128 0.029 0.020 0.015 0.011 0.008 0.001 0.001 0.001 0.000 Actual 0 1 Predicted 1 If required, round your answers to two decimal places. Do not round intermediate calculations. Sensitivity = Specificity = Precision = Actual 0 1 Predicted 1 If required, round your answers to two decimal places. Do not round intermediate calculations. Sensitivity = Specificity = Precision = If required, round your answers to three decimal places. Do not round intermediate calculations. Log odds = Probability of Interest =