# Adjusted R-Squared in terms of variance

Say that I am performing a multiple linear regression with 3 variables. If I want to say that two of these variables account for some percentage of the observed variance in the third variable, should I use my $R ^2$ value, or adjusted $R^2$ value?

I understand that the adjusted R squared value accounts for the fact that I have have more predictors (as compared to a regression of only two variables), but I'm wondering how that translates to my interpretation of the variance in these variables.

• Are you asking about this in the context of assessing multicollinearity? Eg, working up to computing the VIF? – gung May 24 '18 at 12:55
• Possible duplicate of How to split r-squared between predictor variables in multiple regression? – Michael Chernick May 29 '18 at 4:52
• @MichaelChernick it is unclear to me whether the OP want to split $R^2$ or whether it is about the choice between adjusted and unadjusted. Perhaps Matthew can edit to clarify? – mdewey May 29 '18 at 8:45

If you want to describe how much of the total variance in $X_1$ is explained by $X_2$ and $X_3$ using a linear model, then use $R^2$ which by definition gives just this number.
Save the adjusted $R^2$ for when you want to assess if it is worthwhile to include yet another variable, say $X_4$, in an attempt to model $X_1$ more closely, since (regular) $R^2$ will always increase when adding more variables.
You might want to read the wiki-page on the subject, which includes a note on the use of adjusted $R^2$.