I thought that multiple R (e.g. correlation) was ONLY the square root of Multiple R-SQUARED when there was only 1 independent variable.
However, on page 409 (CFA curriculum for Quantatative Methods) question #20 provides the following answer (the data/information set provided for the questions contained more than 1 independent variable )
ANSWER : “The multiple R-squared for the regression is 0.36; thus, the model explains 36 percent of the variation in the dependent variable. The correlation between the predicted and actual values of the dependent variable is the square root of the R-squared or 0.36 ␣ 0.60”
***I understand that I’m probably overthinking, but I feel this is a little misleading. Should I always just assume to take the square root of R-Squared if provided and the question requests correlation on the exam???
Multiple R implies multiple regressors, whereas R-squared doesn’t necessarily imply multiple regressors (in a bivariate regression, there is no multiple R, but there is an R-squared [equal to little-r-squared]).
Multple R is the coefficient of multiple correlation and R-squared is the coefficient of determination.
Mathematically, (Multiple R)^2 = R=squared and conversely sqrt(R-squared) = Multiple R.
Bottom line, there is no Multiple R for a bivariate regression.
If the question asks you to determine how well the independent variables predict the dependent variable (where a value of 1 means perfect predictions versus actual values), just take the sqrt of R-squared (like you said).