CA Foundation · Quantitative Aptitude · Correlation and Regression
For a sample of firms, the regression coefficient of y on x is 1.6 and the regression coefficient of x on y is 0.4. What is the value of the correlation coefficient r, given that both coefficients are positive?
The correlation coefficient is 0.80. It is the geometric mean of the two regression coefficients: the square root of 1.6 × 0.4 = 0.64 is 0.8, taking the positive sign because both regression coefficients are positive.
- A0.64
- B0.80Correct
- C1.00
- D0.50
Explanation
r² = byx × bxy = 1.6 × 0.4 = 0.64, so r = √0.64 = 0.8, positive since both coefficients are positive. The value 0.64 is wrong because it is r² and the square root was not taken.
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