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Focusing on statistical significance (e.g., P value < .05) is misguided.
You did not tell us how much the regression coefficients changed,
when age was added to the model. Did they also reverse signs?
What is the interpretation of the coefficients when age is in the model? If it makes more sense to adjust for age
, then I would not worry about the model w/o the age term.
These are more important to think about than obsessing over the magnitude of P values.
There are several possible causes. First, there are independent variables that are correlated (multicollinearity). Correlated variables can be detected by using the VIF (variance inflation factor) statistics of full regression models. Independent variables with high VIF were the cause multicollinearity. Second, select the best regression model use a stepwise regression or best subset regression, etc.
Independent variables that should theoretically exist in the model needs to be maintained in the selection of the best model.