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Which of the following show the proportion of variance shared between two variables ?

  • A.Coefficient of determination
  • B.Standard error
  • C.Correlation
  • D.ANOVA

Answer: A

The proportion of shared variance is shown by the coefficient of determination.

The coefficient of determination, \(r^{2}\), is the square of the correlation coefficient. It gives the proportion of the variance in one variable that is accounted for by its linear relationship with the other. For example, if r = 0.7, then \(r^{2}\) = 0.49, so 49 percent of the variance is shared.

The correlation coefficient itself shows the direction and strength of the relationship but not the proportion of variance. The standard error measures the precision of an estimate, and ANOVA compares group means.

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