For the variables X, Y and Z, r_xy = 0.80, r_xz = 0.64, and r_yz = 0.79, the square of multiple correlation coefficient \(\rm \mathop R\nolimits_{xyz}^2 \) is:

The square of the multiple correlation coefficient is 0.64.

Key Points

• The multiple correlation coefficient (R) is a statistic that measures the strength of the relationship between multiple independent variables and a dependent variable.
• The square of the multiple correlation coefficient (R^2) is a measure of the proportion of variation in the dependent variable that is explained by the independent variables.
• The formula for \(R^2_{xyz}\) in terms of the pairwise correlations \(r_xy, r_yz , r_zx\) given by \(R^2_{xyz} = \frac{r_{xy}^2 + r_{xz}^2 - 2r_{xy} r_{xz} r_{yz}}{1 - r_{yz}^2} \)
•  \(r_{xy}\) = 0.80, \(r_{xz}\) = 0.64, and \(r_{yz}\) = 0.79
• By putting the value of above variable in the equation. 
•  the square of the multiple correlation coefficient \(R^2_{xyz} =\) 
  is approximately: 0.6386 or 0.64
   

​ Additional Information

• In this case, the square of the multiple correlation coefficient of 0.64 means that 64% of the variation in the dependent variable can be explained by the combination of the independent variables X, Y, and Z.