CA Foundation · Quantitative Aptitude · Correlation and Regression
For a set of paired observations the coefficient of correlation between advertising spend and sales is r = -0.8. What percentage of the variation in sales is explained by the linear relationship with advertising spend?
The coefficient of determination is r squared, which equals 0.64 for r = -0.8. So 64% of the variation in sales is explained by advertising spend. The negative sign disappears on squaring, and the other 36% remains unexplained.
- A64%Correct
- B80%
- C36%
- D-64%
Explanation
The coefficient of determination is r², which is (-0.8)² = 0.64, so 64% of the variation is explained. Option 80% wrongly uses |r| directly. Option 36% is the unexplained share (1 - r²). A percentage of variation cannot be negative, so -64% is impossible.
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