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CA Foundation · Quantitative Aptitude · Correlation and Regression

For a bivariate data set, the regression coefficient of Y on X is 1.6. Which of the following values CANNOT be the regression coefficient of X on Y for the same data?

The value 0.9 is impossible because the product of the two regression coefficients equals r squared and cannot exceed 1. With byx equal to 1.6, bxy cannot exceed 0.625, and 1.6 times 0.9 is 1.44, which is more than 1.

  1. A0.25
  2. B0.5
  3. C0.6
  4. D0.9Correct

Explanation

The product of the two regression coefficients equals r², which cannot exceed 1. With byx = 1.6, bxy must be at most 1/1.6 = 0.625. A value of 0.9 gives a product of 1.44, which is impossible. The other three values give products 0.4, 0.8 and 0.96, all valid.

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