I have a logistic regression model with a dichotomous response variable and predictors coded from $1$ to $10$ and from $0$ to $18$.
When I fit the model, I get these results:
Intercept 2.467 (p=2e-16) Predictor#1 -0.181 (p=1.76e-07) Predictor#2 -0.098 (p=3.34e-14) Null deviance 2252.3 on 1741 DF Residual dev. 2113.1 on 1739 DF (1276 obs. deleted due to missingness) — AIC: 2119.1
And a Nagelkerke $R^2$ of $0.10$. The $R^2$ and the Deviance show the model as a very bad one, but when I calculate the predicted values I get a possibility of $24.8\%$ when both predictors are $1$, and of $89.9\%$ when the predictors are at their maximum values ($10$ and $18$, respectively).
How can I get such bad measures of the goodness of fit, and, at the same time, get such a big difference (statistical significance, $p<0.01$) in the predicted values?