SECTION 17.1 Summary

• Logistic regression explains a success-or-failure response variable in terms of at least one explanatory variable.
• If is a proportion of successes, then the odds of a success are , the ratio of the proportion of successes to the proportion of failures.

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• The simple logistic regression model relates the proportion of successes in the population to one explanatory variable through the logarithm of the odds (or logit) of a success:

  That is, each value of gives a different proportion of successes. The data are values of , with observed success or failure for each. The model assumes that these success-or-failure trials are independent, with probabilities of success given by the logistic regression equation. The parameters of the model for one explanatory variable are and .

• Software fits the data to the model, producing estimates and of the parameters and ,
• The odds ratio is the ratio of the odds of a success at to the odds of a success at x. It is found as , where is the slope in the logistic regression equation.