Logistic regression: overview
This page offers structured overviews of one or more selected methods. Add additional methods for comparisons by clicking on the dropdown button in the righthand column. To practice with a specific method click the button at the bottom row of the table
Logistic regression 


Independent variables  
One or more quantitative of interval or ratio level and/or one or more categorical with independent groups, transformed into code variables  
Dependent variable  
One categorical with 2 independent groups  
Null hypothesis  
Model chisquared test for the complete regression model:
 
Alternative hypothesis  
Model chisquared test for the complete regression model:
 
Assumptions  
 
Test statistic  
Model chisquared test for the complete regression model:
The wald statistic can be defined in two ways:
Likelihood ratio chisquared test for individual $\beta_k$:
 
Sampling distribution of $X^2$ and of the Wald statistic if H0 were true  
Sampling distribution of $X^2$, as computed in the model chisquared test for the complete model:
 
Significant?  
For the model chisquared test for the complete regression model and likelihood ratio chisquared test for individual $\beta_k$:
 
Waldtype approximate $C\%$ confidence interval for $\beta_k$  
$b_k \pm z^* \times SE_{b_k}$ where $z^*$ is the value under the normal curve with the area $C / 100$ between $z^*$ and $z^*$ (e.g. $z^*$ = 1.96 for a 95% confidence interval)  
Goodness of fit measure $R^2_L$  
$R^2_L = \dfrac{D_{null}  D_K}{D_{null}}$ There are several other goodness of fit measures in logistic regression. In logistic regression, there is no single agreed upon measure of goodness of fit.  
Example context  
Can body mass index, stress level, and gender predict whether people get diagnosed with diabetes?  
Pratice questions  