CA Foundation · Quantitative Aptitude · Correlation and Regression
The coefficient of correlation between a firm's advertising expenditure and its sales is −0.6. What percentage of the variation in sales is NOT explained by the linear relationship with advertising expenditure?
The unexplained variation is 64%. The coefficient of determination is r² = 0.36, meaning 36% of the variation in sales is explained by advertising. The remainder, 100% − 36% = 64%, is unexplained. The sign of r does not matter here.
- A36%
- B64%Correct
- C60%
- D40%
Explanation
The coefficient of determination is r² = (−0.6)² = 0.36, so 36% of the variation is explained. The unexplained part is 1 − 0.36 = 0.64, that is 64%. The option 36% is the explained share, not the unexplained share.
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