Polynomial Regression

Question

I was doing a regression from some data points I have, and I was considering which kind of regression would give the most accurate model by looking at the R^2 value excel calculated from each type of regression. However, I noticed that when the order of the polynomial is equal to the amount of data points I have, the R^2 value will always be equal to 1. Although this makes mathematical sense, should I avoid using the R^2 value for non-linear regression? In which, case what should I use? (Looking at the fifth polynomial graph, it doesn't look like a good model. How do I determine which one is better then, if not with the R^2?)

Answer 1

If you want to use something like the $R^2$, consider the adjusted one.

Using you data

• For a linear regression, you will get $0.925431$
• For a quadratic regression, $0.933753$
• For a cubic regression, $0.904233$

So, stop at the quadratic.