CMA Foundation · Fundamentals of Business Mathematics and Statistics · Correlation and Regression
The regression lines of Y on X and X on Y are Y = 0.8X + 10 and X = 0.45Y + 5 respectively. What is the value of the correlation coefficient?
The correlation coefficient is 0.6. It is the square root of the product of the two regression coefficients, 0.8 × 0.45 = 0.36, and its sign is positive because both coefficients are positive. The figure 0.36 is only r squared.
- A0.36
- B0.6Correct
- C−0.6
- D0.8
Explanation
b_yx = 0.8 and b_xy = 0.45. r² = 0.8 × 0.45 = 0.36, so r = 0.6. Both coefficients are positive, so r is positive, which rules out −0.6. The value 0.36 is r² and was not square-rooted.
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