ACCA Applied Skills · Performance Management · Analytical techniques in budgeting and forecasting
A analyst finds that the coefficient of determination between a retailer's weekly sales and the number of staff on duty is 0.49, and that the regression line slopes upwards. What is the correlation coefficient?
The correlation coefficient is +0.70. It is the square root of the coefficient of determination, 0.49, and takes the sign of the regression slope. Because the line slopes upwards the relationship is positive, so the negative root is rejected.
- A+0.70Correct
- B-0.70
- C+0.24
- D+0.49
Explanation
r is the square root of r squared: the square root of 0.49 is 0.70. The upward slope means the relationship is positive, so r = +0.70. -0.70 ignores the slope direction. 0.24 halves 0.49, and 0.49 treats r squared as r.
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