When calculating Adjusted $R^2$ the formula is $1-(1-R^2)\frac{n-1}{n-k-1}$ with $k$ being how many predictors you have. If I am using a model with a single variable but that variable has been put to the 4th, 3rd, and 2nd power like the following,


would I have a single predictor or would I count each powered term as a predictor? Also if you could give short reasoning so I can try and grasp the concept as to why or why not to.

Thanks in advance.


Yes, each term counts as a predictor. What you're doing is fitting a model with 5 parameters (4 plus the intercept). To make this more clear, as far as the fitting is concerned you have constructed a new set of variables $x_1 = x$, $x_2 = x^2$, ... $x_4 = x^4$ and you have fitted a regression with $x_1$ to $x_4$ as predictors.

  • 2
    $\begingroup$ Thank you Glen, as a counter question is the intercept counted as a predictor with Adjusted $R^2$? $\endgroup$ – DanTheMan Oct 24 '12 at 21:51
  • 1
    $\begingroup$ @DanTheMan I believe the "-1" in the numerator and denominator of the formula is intended to account for the intercept. $\endgroup$ – Glen_b -Reinstate Monica Oct 25 '12 at 1:06

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.