CA Foundation · Quantitative Aptitude · Correlation and Regression
Two regression lines of a sample are 4x − 5y + 33 = 0 and 20x − 9y = 107. Taking the first as the regression of Y on X, what is the coefficient of correlation between X and Y?
The correlation coefficient is 0.6. Writing the lines in regression form gives byx equal to 0.8 and bxy equal to 0.45. Their product is 0.36, whose square root is 0.6, and the sign is positive because both regression coefficients are positive.
- A0.6Correct
- B0.75
- C0.8
- D0.9
Explanation
First line gives y = (4x + 33)/5, so byx = 0.8. Second line gives x = (107 + 9y)/20, so bxy = 9/20 = 0.45. Then r² = 0.8 × 0.45 = 0.36, so r = 0.6 (positive since both coefficients are positive). The value 0.8 is just byx, not r.
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