# Multiple R squared

Can someone explain the significance of this term in an ANOVA table? If a question asks that you interpret or use R squared, which would you focus on R squared or multiple?

I understand R Squared to be the percent variation in Y that can be explained by the regression model. The higher the R squared the better (though not all the time…multicolliearity will give an unusually high R squared but the coefficients will usually be insignificant).

Also, please correct me if I am wrong, but you should also be aware of the adjusted R squared, which basically states that adding more independent variables will of course raise the R squared, but the adjusted R squared will reduce these effects?

with a single independent variable, multicolliearity doesnt exist so a high R2 is very good. Single X: Multiple R = correlation R^2 = coeff of Determination **R^2 = corr^2 Multi-regression: Multiple R-Squared = corr^2

R2 will keep on increasing as you add more independent variables. There will be a time where adding new variables will lead to diminishing returns. This is where adjusted R2 is helpful. Adjusted R2 will always be lower than R2