CMA Foundation · Fundamentals of Business Mathematics and Statistics · Correlation and Regression
The covariance between advertising spend (X) and sales (Y) of a firm is 36. The standard deviations are σx = 6 and σy = 10. What is the coefficient of correlation, and how is the relation described?
The correlation is 0.60, a moderately strong positive correlation. It is found by dividing the covariance 36 by the product of the standard deviations, 6×10 = 60, giving 0.6; the positive sign shows advertising and sales move in the same direction.
- A0.60, positive correlationCorrect
- B0.60, negative correlation
- C6.00, perfect positive
- D0.36, low positive
Explanation
r = Cov/(σxσy) = 36/(6×10) = 0.6. Positive sign means both variables move in the same direction. A value of 6 is impossible since r lies between −1 and +1.
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