In multiple logistic regression the response variable has two possible values, as in logistic regression, but there can be several explanatory variables.
As in multiple regression, there is an overall test for all the explanatory variables. The null hypothesis that the coefficients for all the explanatory variables are zero is tested by a statistic that has a distribution that is approximately χ2 with degrees of freedom equal to the number of explanatory variables. The P-value is approximately P(χ2≥X2).
Hypotheses about individual coefficients,H0:βj=0 or H0:eβj=1 in terms of the odds ratio, are tested by a statistic that is approximately χ2 with 1 degree of freedom. The P-value is approximately P(χ2≥X2). As in multiple regression, these tests assess the contribution of each explanatory variable given the other explanatory variables are already in the model.