Question

# Why is it important to use adjusted r2 rather than r2 (the coefficient of determination) when...

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 ?

cant afford to get it wrong :(

Thank you

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.

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