I have a feeling that this is a stupid question, but googling around I haven't found an answer to it.
Simply: What does it mean if a multiple regression model is significant but none of the individual predictors are significant? There are between 5 and 10 predictors in the model.
I would imagine that it's because of the high number of predictors in the model. One of the predictors almost passed the threshold of significance (p = .06). Most of the predictors, when isolated in separate simple regression models with the same independent variable, have significant p-values. In other words, the simple regression model with predictor A and variable Z is significant, the simple model with predictor B and variable Z is significant, etc., but the multiple regression model with predictors A, B, etc., and variable Z is non-significant.
My other thought would be multicollinearity, but I tested all of the assumptions, and the multiple regression model meets them. In particular, I tested for multicollinearity with the “vif()” function in R. As far as I understand, a VIF value over 5 or 10 for any predictor indicates a problematic level of multicollinearity. For this multiple regression model, none of the predictors exceeded a VIF value of 5. If it matters, the VIF values for each variable were: 2 2 4 4 1 2 1.5 and 3.5.
For theoretical reasons, I would expect there to be an overlap between the predictors, because there are theoretically causal relationships between some of the predictors that were used.
Thanks in advance. :)
