Notice that the logit transformation g(x) has linear parameters (b- values) and may be continuous with unrestricted range. Using these functions, a binomial error distribution is found with y = π(x) + Ɛ. The solution to a logistic regression model is to find the b- values that “best” predict the dichotomous y variable based on the values of the numeric x variables.
The logit transformation function is chosen because of its mathematical power and simplicity, and because it lends an intuitive understanding to the coefficients eventually created in the model. The following equations describe the logistic regression model, with π(x) being the probability that the dependent variable is 1, and g(x) being the logit transformation: