Can Hosmer-lemeshow chi-square statistic explain calibration? I'm doing a logistic regression and created a calibration plot. I also conducted a Hosmer-Lemeshow test and got the corresponding chi-square. Is there any relationship between the calibration plot and the chi-square? It is reasonable to put the chi-square value on the calibration plot (to show the result)?

I'd think it's reasonable. The Hosmer-Lemeshow statistic is pretty closely related to the calibration plot; it basically makes the same comparison that the calibration plot allows as well. However, the relation is not totally direct; the Hosmer-Lemeshow binning into groups is not usually shown on the calibration plot (although I think there is more than one way to set it up). So one can't directly connect the workings of the test to the plot. Where what is presented and how closely the connection needs to be between things that are presented together is to some extent a matter of taste. I think it's fine to put them together.
