CMA Foundation · Fundamentals of Business Mathematics and Statistics · Correlation and Regression
The coefficient of correlation between the advertising spend and sales of a Pune-based firm is 0.8. What percentage of the variation in sales is explained by variation in advertising spend?
Sixty-four percent of the variation in sales is explained by advertising spend. The coefficient of determination is the square of the correlation coefficient, so 0.8 squared gives 0.64. The remaining 36 percent is unexplained variation due to other factors, so 80 percent is not correct.
- A80%
- B64%Correct
- C36%
- D16%
Explanation
The coefficient of determination is r squared = 0.8 x 0.8 = 0.64, so 64% of the variation in sales is explained by advertising. Choosing 80% wrongly treats r itself as the explained share. 36% is 1 - r squared, the unexplained part.
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