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 100 prospective dates to indicate whether there was any interest in learning more about them.

Oollama has split the 100 profiles rated “interested” or “not interested” by Erin into a training set of 60 observations and a validation set of 40 observations. Oollama then trained a logistic regression to predict Erin’s interest in other profiles that Erin has not yet viewed. The resulting logistic regression model is as follows:

For 40 profiles (observations) in the validation set, 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 validation 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 lift charts to evaluate their classification models. For these data, what is the lift resulting from the logistic regression model on the top 25% of profiles that Erin is most likely to be interested in? 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.

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Log Odds of Interested = -0.920 +0.325 Fitness 3.611 Music +5.535 Education 2.927 Alcohol