CA Foundation · Quantitative Aptitude · Correlation and Regression
For a bivariate data set, the regression coefficient of y on x is 0.9 and that of x on y is 0.4. What is the coefficient of correlation between x and y?
The correlation coefficient is 0.60. It equals the geometric mean of the two regression coefficients, √(0.9 × 0.4) = √0.36 = 0.6. The sign is positive because both regression coefficients are positive.
- A0.60Correct
- B0.65
- C0.36
- D0.50
Explanation
The correlation coefficient is the geometric mean of the two regression coefficients: r = √(0.9 × 0.4) = √0.36 = 0.6. Both coefficients are positive, so r is positive. Option 0.65 is the arithmetic mean, and 0.36 is r² rather than r.
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