# Should I remove non-significant variables from my regression model

I have run a multiple linear regression using stepwise regression to select the best model, however the best model returned has a non-significant variable. When I remove this the AIC value goes up indicating the model without the significant variable is a worse fit. Should I remove the non-significant predictor or should I leave it in as it is a better model?

• What is your goal here? Prediction or explanation? How big is your data? – TrynnaDoStat Jan 18 '15 at 15:09
• Thanks for your answer below. My goal is prediction and my data set has 590 cases. – Poppy Jan 18 '15 at 16:44
• I give a detailed list of the problems with stepwise model building in my answer here: stats.stackexchange.com/questions/115843/…. – Alexis Jan 19 '15 at 1:01
• Suppressor variables are often not significant, yet they can affect fit-statistics a lot. Might be interesting to check for suppressor effects (especially with a view to model interpretation). – StatisticsRat Mar 15 '17 at 16:35

Leave it in. The data are incapable of really telling you which model is "better" unless you use AIC in a highly structured way (e.g. on a pre-specified large group of variables), and removing insignificant variables invalidates the estimate of $\sigma^2$ and all $P$-values, standard errors, and confidence limits in addition to invalidating the formula for adjusted $R^2$. Much is written about these issues on this site.