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If 'r' is the correlation coefficient and byx and bxy are the regression coefficients of the regression lines y on x and x on y respectively, then r =

  • A.\(b_{xy} \times b_{yx}\)
  • B.\(\sqrt{b_{xy} / b_{yx}}\)
  • C.\(\sqrt{1 - b_{xy} b_{yx}}\)
  • D.\(\sqrt{b_{xy} b_{yx}}\)

Answer: D

The correlation coefficient is the geometric mean of the two regression coefficients: r = \(\sqrt{b_{xy} \times b_{yx}}\), with the sign of the coefficients. Option (A) is their product, which equals r squared and not r. Option (B) takes a ratio, and (C) has a form that does not occur. So (D) is the answer.

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