Logistic Regression

Linear Regression

Purchases vs. Income

R Graphical Parameters

Purchase Dataset Conceptually, if a person has greater income, the probability that he or she will purchase is greater than if the person has less income.

Categorical with a Linear Model

Residual vs.Fitted

Categorical Dependent Variable Binary Data Don’t Prefer Log is better at representing the data

Logistic Regression

The original classification table is put in here to get the Ns as well as to get the original percent among the respondents The original percent is turned into a probability The Average Odds is then multiplied by the Exp of the Beta. Which is then turned back into a percentage The original percentage is subtracted from the predicted percent to determine the change ~1:1 Ratio for getting a No or Yes Logit Model Includes Log; So Need to Convert to Odds 2.52 vs Odds = P / (1-P) Odds – (Odds*P) = P Odds = P + Odds*P Odds = P(1 + Odds) P = Odds / (1 + Odds) Delta from the Average Odds 100%-72% = 28% 72% / 28% = 2.6 The Regression Beta is then converted to Odds. Mathematics

Logistic Regression

Measure of Goodness R^2 ranges from 0 to 1.0, and can be considered as a percentage of variability. An R 2 of 1.0—or 100%—means that 100% of the variance in the dependent variable can be explained by variability in the independent variable or variables. We use the log likelihood as our criterion for the “best” coefficients. The closer to 0.0 a log likelihood: the better the fit the closer you’ve come to maximizing the estimate of the likelihood.

Probability of No Purchase: Person who did not purchase has a 0 on the Purchased variable Predicted probability of 2% that he will purchase Probability of Purchase: Person who did purchase has a 1 on the Purchased variable Predicted probability of 94% that this person will purchase The probabilities are of two different events: No Purchase and Purchase In the first case, it’s 98% that he doesn’t purchase, and he doesn’t.