# Adjusted R squared

Adjusted R^{2} is a corrected goodness-of-fit (model accuracy) measure for linear
models. It identifies the percentage of variance in the target field that is explained by the input
or inputs.

R^{2} tends to optimistically estimate the fit of the linear regression. It always
increases as the number of effects are included in the model. Adjusted R^{2} attempts to
correct for this overestimation. Adjusted R^{2} might decrease if a specific effect does not
improve the model.

Adjusted R squared is calculated by dividing the residual mean square error by the total mean square error (which is the sample variance of the target field). The result is then subtracted from 1.

Adjusted R^{2} is always less than or equal to R^{2}.
A value of 1 indicates a model that perfectly predicts values in the
target field. A value that is less than or equal to 0 indicates a
model that has no predictive value. In the real world, adjusted R^{2} lies
between these values.