Why do we sometimes use r2adj instead of r2 Give an example

Why do we sometimes use r^2_adj instead of r²? Give an example of a case in which you would use r^2_adj instead of r².

Solution

R2 will riseand indicate a better fit as we add more independent variables but often times, the new variables do not help in improving the predictability of the dependent variable but because of the way quants work, the R2 value goes up.

To adjust for this, we calculate adjusted R2 which is just deflated based on N-1/N-k-1 to compensate for the increased number of independent variables.

Unlike R2, the adjusted R2 increases only if the new term improves the model more than would be expected by chance. The adjusted R2 can be negative, and will always be less than or equal to R2.

In any case when we have too many variables to choose from, we will use r2adj, in order to ensure that we are not biased towards picking more variables to increase r2.