 The Sample Multiple Correlation Coefficient, R, is a measure of the strength of the association between the independent (explanatory) variables and the one dependent (prediction) variable.

Interpretation of R

• Strength of the Association:  The strength of the association is measured by the sample Multiple Correlation Coefficient, RR can be any value from 0 to +1.
• The closer R is to one, the stronger the linear association is.
• If R equals zero, then there is no linear association between the dependent variable and the independent variables.

Unlike the simple correlation coefficient, r, which tells both the strength and direction of the association, R tells only the strength of the associationR is never a negative value.  This can be seen from the formula below, since the square root of this value indicates the positive root.

Formula for R

Formula for two independent variables, X1 and X2: For more info on the formula click here.

When we have more than 2 independent variables, it is usually easiest to use matrices for the computations.  A good reference for this is Neter, et al., 1996

 R value Interpretation* 1 perfect linear relationship 0 no linear relationship

No other values of R have precise definitions of strength. See the chart below.

 R value Interpretation 0.9 strong association 0.5 moderate association 0.25 weak association

Learn the procedure for calculating the multiple correlation coefficient   STATS @ MTSU