Coefficient of Determination for High Order Polynomials Because the Coefficient of Determination makes use of the mean of y, is the Coefficient of Determination meaningless for higher order polynomials (higher order than linear polynomials)? I'm assuming this because I think it's easy to visualise how the variation from the mean gives a representation for how much of the variance is not described by the best fit line for linear graphs, but not for, say, fifth or sixth order polynomials.
Coefficient of Determination makes perfect sense for the linear regression of $y$ on $x_1$, $x_2$, ... In particular, it makes sense for the linear regression of $y$ on $x$, $x^2$, ...  -  a polynomial is a LINEAR combination of powers of $x$!
Coefficient of Determination makes perfect sense for the linear regression of $y$ on $x_1$, $x_2$, ... In particular, it makes sense for the linear regression of $y$ on $x$, $x^2$, ...  -  a polynomial is a LINEAR combination of powers of $x$!