# In stepwise regression, how to interpret non-significant variables? [duplicate]

I have more than 15 IVs such as age, gender, education, first language, technology proficiency, health condition, etc, and one of my DVs is health literacy level, which is measured through a standard questionnaire.

I'm using multiple regression to see which IVs might predict my DV. Since I don't have a specific assumption, I chose stepwise regression (forward selection) to find the best model.

I got a model with the lowest AIC. The model is significant (p <.001, R2 = .25) and consists of health condition, first language, technology proficiency, and age. But among the four variables, only the health condition is significant (p = .005), first language, technology proficiency are in the borderline (p =.07 ~ .08), and age is not significant at all. So I'm wondering how I should interpret the two borderline variables and the non-significant variable in this case?

I'm asking this question not only because the two variables are in the borderline, but also they contribute to the best model (i.e., the models without them has higher AIC).

Maybe the way I understand stepwise regression is not correctly, so I should pick another type of analysis. Or Maybe I should run some hierarchical regression (e.g., incremental F test) to see if there are more layers of this relationship. Do anyone have any ideas?

## marked as duplicate by Michael Chernick, mkt, Peter Flom♦Aug 21 at 12:00

• Note that removing variables always reduces $R^2$, whether or not they're relevant. – gung Aug 21 at 20:30