The simple logistic regression model relates the proportion of successes in the population to one explanatory variable x through the logarithm of the odds (or logit) of a success:
log(p1−p)=β0+β1x
That is, each value of x gives a different proportion p of successes. The data are n values of x, with observed success or failure for each. The model assumes that these n 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 β0 and β1.