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Say I'm in a classic linear regression situation:

$Y = \beta_0X_0 + \beta_1X_1 + \dots + \beta_NX_N + \epsilon$

And that I know that my explanatory variables $X$ only explain some part of my regressand $Y$, what sort of metrics could I use to estimate the proportion of this unexplained part? I know about the fraction of variance unexplained (FVU) that can be calculated with the coefficient of determination, but after a quick search on the internet I get the feeling that it's not used that often?

I may be wrong but I'm looking for potential alternative ways of quantifying this unexplained proportion in my system.

DeadKarlMarx
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1 Answers1

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$R^2$ is the proportion of variance explained, at least under particular conditions, which you have.

Consequently, $1-R^2$ would be the proportion of variance left unexplained. While this metric is not as common as $R^2$ (I’d never thought of it before I saw this question), it should not cause controversy.

Dave
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