# Best way to determine contribution of a variable to regression model

What is the best way to determine the degree of contribution a variable is making by its addition to a regression model. Suppose I have following regression model for OutNumeric which is a continuous positive numeric variable.

lm(OutNumeric~Anumeric+Bfactor, data=mydf)


Anumeric is also a positive continuous variable, while Bfactor is a factor variable with only 2 levels. I want to determine the degree of improvement to the model by another positive continuous variable Cnumeric.

lm(OutNumeric~Anumeric+Bfactor+Cnumeric, data=mydf)


I could think of following simple options:

Check R^2
Check AIC, BIC
Run predict on an independent set and see correlation.


However, my main aim is to determine if Cnumeric is an important factor in determination of OutNumeric, rather than prediction.

• "Best" is really not defined here. All your suggestions make sense. Best for your purpose likely exists though. Can you provide more details of your goal/investigation? Some things you probably already know: If all you care about is having a highly determined model, then partial $R^2$ makes sense. Along the same lines, an F value greater than 1 for that predictor means it accounts for more error than a randomly chosen variable (there may be a better way to phrase that), and a significant F tells you it likely doesn't have 0 contribution. AIC of course balances predictiveness with complexity. May 7, 2015 at 14:35