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CA Foundation · Quantitative Aptitude · Correlation and Regression

Which of the following pairs of regression coefficients (b_yx, b_xy) could possibly arise from the same set of bivariate data?

The pair (0.5, 0.6) is possible. The two regression coefficients must share the same sign, and their product, which equals r², must not exceed 1. Here the product is 0.30. The other pairs either have opposite signs or a product above 1.

  1. A(0.5, 0.6)Correct
  2. B(0.8, 1.5)
  3. C(−0.4, 0.9)
  4. D(−1.2, −0.9)

Explanation

Both regression coefficients must have the same sign, and their product equals r², which cannot exceed 1. For (0.5, 0.6) the product is 0.30, which is valid. (0.8, 1.5) gives 1.2 and (−1.2, −0.9) gives 1.08, both above 1. (−0.4, 0.9) has opposite signs, which is impossible.

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