Multiple logistic regression models


Am I correct in saying that if my results from multiple logistic regression show that the full model does not differ significantly from the "constant only" model (i.e P > 0.05 in LR goodness of fit test), then I should not read too much into individual predictor variables which have statistically significant coefficients (i.e. P < 0.05 for P>z)?

Also, if I want to control for the effect a confounding factor (e.g. gender) on a binary response variable (e.g. reads Time magazine yes/no) in relation to the predictor variable of interest (e.g. level of education), I assume I do this by including both gender and education as predictor variables. However, if the p value for gender is not significant when I run the model, but is for education, can I assume gender has no effect on the relationship between education and whether or not a person reads Time magazine, and therefore drop it from the model?

For the first part, are you saying that your full model has all of your independent variables in it and that your "constant only" model is a null model (one with no predictors)? Guess I'm confused.

For the second part, normally, social scientists don't throw away variables just for parsimony (like statistisicans do). We care about all variables, even if they are not significant. So keep both because if you go around adding or subtracting variables, you may affect other variables and/or the overall model's significance. Use all variables that make sense for your research question.
Yes, full modell has all predictors and "contant only" model is the null model. Non significant LR test means that the model with the predictors added was not a significat improvement on the null model. But what if some of the individual predictiors are significant nevertheless?

Re the second question, thanks for the insight.
1- If the model is not fit, then you can not rely on the results as this indicate that the model prediction of criterion variable is close to the chance.

2- If you have a dichotomous variable and a continuous one to be correlated while adjusting (or controlling other variables), you can simply use partial correlation!!