The Hosmer and Lemeshow test

This test is a type of chi-square test. It indicates the extent to which the estimated model provides a better fit to the data (i.e. has better predictive power) than the null model. The test will produce a p-value: if the p-value is above 0.05 (statistically non-significant) the estimated model has adequate fit, and if the p-value is below 0.05 (statistically significant) the estimated model does not adequately fit the data.   

More information
help estat gof

Practical example

Let us first go back to the example from the multiple linear regression analysis. The quietly option is included in the beginning of the command to suppress the output. 

quietly logistic earlyret bmi sex ib1.educ if pop_logistic==1

And then we run the test: 

estat gof

The p-value for the test (Prob > chi2) is above 0.05, suggesting that the estimated model has adequate fit.