What does the multiple correlation coefficient R measure?

What does the multiple correlation coefficient R measure?

• A. The linear slope between Y and a single predictor.
• B. The correlation between the dependent variable and the independent variables; the differences between predicted and actual data.
• C. The variance of residuals.
• D. The standard error of the estimate.

Answer: (B)

The multiple correlation coefficient captures how well the set of predictors together can predict the outcome. It’s the strength of the relationship between the observed Y and the model’s predicted Y (the Ŷ values obtained from the regression). When the predictors explain a lot of the variation in Y, the predicted values align closely with the actual values, and R is large (with R^2 showing the proportion of variance in Y explained). This is different from a single-slope effect, which describes one predictor, and from residual variance or the standard error of the estimate, which reflect error magnitude rather than the overall predictive strength.

The multiple correlation coefficient captures how well the set of predictors together can predict the outcome. It’s the strength of the relationship between the observed Y and the model’s predicted Y (the Ŷ values obtained from the regression). When the predictors explain a lot of the variation in Y, the predicted values align closely with the actual values, and R is large (with R^2 showing the proportion of variance in Y explained). This is different from a single-slope effect, which describes one predictor, and from residual variance or the standard error of the estimate, which reflect error magnitude rather than the overall predictive strength.