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CA Foundation · Quantitative Aptitude · Correlation and Regression

The two regression lines obtained from a sample are 2x – 5y + 20 = 0 and 10x – 9y = 28. Assuming the lines are correctly assigned so that r² ≤ 1, what is the correlation coefficient between x and y?

The correlation coefficient is 0.6. Treating the first line as y on x gives byx = 0.4, and the second as x on y gives bxy = 0.9. Their product is 0.36, so r = √0.36 = 0.6, positive because both coefficients are positive.

  1. A–0.6
  2. B0.36
  3. C0.6Correct
  4. D0.75

Explanation

Take 2x – 5y + 20 = 0 as y on x: y = 0.4x + 4, so byx = 0.4. Take 10x – 9y = 28 as x on y: x = 0.9y + 2.8, so bxy = 0.9. Then r² = 0.4 × 0.9 = 0.36, so r = 0.6, and it is positive because both coefficients are positive. The reverse assignment gives bxy = 2.5 and byx = 10/9, whose product exceeds 1, so it is impossible. Choosing 0.36 forgets the square root, and –0.6 has the wrong sign.

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