Interpretation of R-squared
Experimenters frequently ask the question “What is a good R-squared value? How low can it be before the results are not valid?”
First of all, experimenters should be focusing on the adjusted R-squared and predicted R-squared values. The regular R-squared can be artificially inflated by simply continuing to add terms to the model, even if the terms are not statistically significant. The adjusted R-squared plateaus when insignificant terms are added to the model, and the predicted R-squared will decrease when there are too many insignificant terms. A rule of thumb is that the adjusted and predicted R-squared values should be within 0.2 of each other.
There is no commonly used “cut-off” value for R-squareds. Analysis must include information from all of the available statistics.
If the model is significant, lack of fit insignificant, there is good agreement between adjusted and predicted R2, adequate precision is over 4 and the residuals are well behaved; then the model provides good predictions for AVERAGE outcomes. A low R-squared indicates there is individual variation that is not explained by the current model.