# Using Pearson's $R^2$ for model selection

I have a question about using $R^2$ as a "best fit" technique for cross-sectional (not time series) type data...

Suppose you have a data set, and you're trying to fit a regression model to it. You try several types of models (classic linear, exponential, log-log, etc), and ultimately choose one with the highest $R^2$ value (unadjusted?).

Is this an appropriate way to select a regression model, or are there other, more appropriate ways to determine the model which best fits the data?

Thanks

• In this case, you will pick a model with as many parameters as observations, leading to the optimal R squared of 1. By including many high order polynomials of the predictors and their interactions, this is easy to achieve. – Michael M Jul 14 '15 at 19:04

I'll flesh this out a bit more: $R^2$ is useful in establishing how well a line fits data. It is defined as $$R^2:=1 - \frac{\text{Sum of vertical distances from the line of best fit}}{\text{Sum of horizontal distances from the line of best fit}}$$ This quantity works well in linear cases because it is bounded by 0 and 1; but for your purposes, e.g. exponential fits, there is no such guarantee of behavior of your data and so $R^2$ isn't such a good metric.
EDIT: See the answer in this post as to why $R^2$ is insufficient.