Question

Why is it important to use adjusted r² rather than r² (the coefficient of determination) when comparing the fit of different regression models with the same dependent variable ?

need help answering this question

cant afford to get it wrong :(

Thank you

Answer 1

R² or the coefficient of determination represents the proportion of variance of depend variable that has been explained by the independent variables in the model.

If R²=90% , this means that 90% of the increase in depend variable is due to increase in independent variable.

One limitation of R² is that it increases by adding independent variables to the model which is misleading since some added variables might be useless. To overcome this limitation we use Adjusted R² .

Adjusted R² is modified version of the R² and takes into account the number independent variables in the model.

Adjusted R² will only increase if the added independent variable is useful for improving the model otherwise decrease.