# Normalizing R2 for using with cross-validation

The coefficient of determination, denoted as \(R^2\), is commonly used in evaluating the performance of predictive models, particularly in life sciences. It indicates what proportion of variance in the target variable is explained by model predictions.

\(R^2\) takes values between minus infinity and one, the higher – the better. If tested on the same data as the model was fitted, zero means that the performance is the same as naïve baseline always predicting a constant.

When using \(R^2\) with leave-one-out cross-validation, we need to normalise the score as otherwise the naïve baseline is below zero (more details can be found in our ArXiv note). The normalisation depends only on the number of data points in cross-validation, and is

$R^2_{\mathit{CV}} = \frac{R^2 - R^2_N}{1 - R^2_N}$,

where

$R^2_N = 1 - \frac{n^2}{(n-1)^2}$,

where $n$ is the number of data points.