# Probit Regression and Transformation

In the probit regression model, the predicted values for the dependent variable will never be less than (or equal to) 0, or greater than (or equal to) 1, regardless of the values of the independent variables; it is, therefore, commonly used to analyze binary dependent or response variables (see also the binomial distribution). This is accomplished by applying the following regression equation (the term probit was first used by Bliss, 1934):

y = NP(b0 + b1*x1 ...)

where NP stands for normal probability (space under the normal distribution; or cumulative distribution function of the normal distribution). One can easily recognize that, regardless of the regression coefficients or the magnitude of the x values, this model will always produce predicted values (predicted y's) in the range of 0 to 1.

For additional details, see also the Nonlinear Estimation or Generalized Linear/Nonlinear Models module; see also Logit Transformation and Regression and Multinomial Logit and Probit Regression for similar transformations.