1. Dating Web Site (logistic regression). 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:
Log Odds of Interested = −0.920  0.325  Fitness − 3.611  Music 5.535  Education − 2.927  Alcohol 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 5 3, Music 51, Education 5 3, and Alcohol 51. Use the estimated logistic regression equation to compute the probability of Erin’s interest in this profile.

d. Now that Oollama has trained a logistic regression model based on Erin’s initial evaluations of 40 profiles, what should its next steps be in the modeling process?

Probability of Observation Interested Interested Observation Interested 35 1 1.000 13 21 1 0.999 29 1 0.999 23 2 25 1 0.999 7 39 1 0.999 9 26 1 0.990 12 23 1 0.981 18 33 1 0.974 22 1 0 0.882 31 24 1 0.882 6 28 1 0.882 20 36 1 0.882 15 16 0 0.791 27 1 0.791 14 30 1 0.791 19 32 1 0.791 8 34 1 0.791 10 37 1 0.791 17 40 1 0.791 4 38 1 0.732 11 O o O o O O - - O O O O O O O O O O O 255 Probability of Interested 0.412 0.285 0.219 0.168 0.168 0.168 0 0.168 1 0.168 1 0.168 0 0.128 0.128 0.029 0.020 0.015 0.011 0.008 0.001 0.001 0.001 0.000