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CA Foundation · Quantitative Aptitude · Correlation and Regression

The two regression lines of a sample are 4x − 5y + 33 = 0 and 20x − 9y = 107. What is the value of the correlation coefficient between x and y?

The correlation coefficient is 0.60. The only valid assignment gives byx = 0.8 and bxy = 0.45. Their product is 0.36, and its positive square root is 0.60. The sign is positive because both regression coefficients are positive.

  1. A0.60Correct
  2. B0.36
  3. C0.45
  4. D0.80

Explanation

Take 4x − 5y + 33 = 0 as y on x, so byx = 4/5 = 0.8. Take 20x − 9y = 107 as x on y, so bxy = 9/20 = 0.45. The reverse assignment gives bxy = 5/4 and byx = 20/9, whose product exceeds 1, which is impossible. So r² = 0.8 × 0.45 = 0.36 and r = 0.60, positive because both coefficients are positive. The value 0.36 is r², not r.

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