Linear Regression - Different R-Squared & Adj R Squared in Report and Interactive outputs

joacoachinelli

Hi everyone!

I´m running a simple Linear Regression, and when I look at the outputs, I get different values for R-Squared and Adj. R-Squared between the Report and the Interactive outpus.

Which should I take as valid? And why is that difference?

Thanks!

AngelosPachis

Hi @joacoachinelli,

I think you should use the adjusted R-Squared when you are comparing models that use different number of predictors. That is and I quote from a website

"

The adjusted R-squared compares the explanatory power of regression models that contain different numbers of predictors.

Suppose you compare a five-predictor model with a higher R-squared to a one-predictor model. Does the five predictor model have a higher R-squared because it’s better? Or is the R-squared higher because it has more predictors? Simply compare the adjusted R-squared values to find out!

The adjusted R-squared is a modified version of R-squared that has been adjusted for the number of predictors in the model. The adjusted R-squared increases only if the new term improves the model more than would be expected by chance. It decreases when a predictor improves the model by less than expected by chance. The adjusted R-squared can be negative, but it’s usually not. It is always lower than the R-squared.

"

So generally, trust the adjusted r-square if you compare for example between two models, the one using 2 predictors and the other 4; use the adjusted R-squared to get a fair comparison between the two models.

Hope that helps in a way,

Cheers,

Angelos