# Interpreting the predicted R-squared (R-Sq(pred)) in the regression output - ID 983

Revised: 12/12/2011

Applies to

• Minitab 16

#### Description

How do I interpret the predicted R-squared value in my regression output?

#### Solution

Predicted R-squared is used in regression analysis to indicate how well the model predicts responses for new observations, whereas R-squared indicates how well the model fits your data. Predicted R-squared can prevent overfitting the model and can be more useful than adjusted R-squared for comparing models because it is calculated using observations not included in model estimation. Overfitting refers to models that appear to explain the relationship between the predictor and response variables for the data set used for model calculation but fail to provide valid predictions for new observations.

Predicted R-squared is calculated by systematically removing each observation from the data set, estimating the regression equation, and determining how well the model predicts the removed observation. Predicted R-squared ranges between 0 and 100% and is calculated from the PRESS statistic. Larger values of predicted R-squared suggest models of greater predictive ability.

For example, you work for a financial consulting firm and are developing a model to predict future market conditions. The model you settle on looks promising because it has an R-squared of 87%. However, when you calculate the predicted R-squared you see that it drops to 52%. This may indicate an overfitted model and suggests that your model will not predict new observations nearly as well as it fits your existing data.

Note: You can find this information in the Minitab Glossary. Choose Help > Glossary. On the Index tab, in Type in the keyword to find, type r-sq, and then double-click on R-squared predicted in the list below.

To view the formula for the predicted R-squared, see Knowledgebase ID 922.

Note: You can get the predicted R-squared using Stat > Regression > Regression > Options or Stat > Regression > Stepwise > Options.

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