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

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


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