CA Foundation · Quantitative Aptitude · Correlation and Regression
The coefficient of correlation between the number of hours of training and error rate among clerks at a Chennai firm is -0.8. What percentage of the variation in the error rate is explained by variation in training hours?
64% of the variation is explained. The proportion explained by the linear relationship is the square of the correlation coefficient, (-0.8)² = 0.64. The negative sign only shows the direction. The 36% figure is the unexplained part, and 80% wrongly uses r itself.
- A64%Correct
- B80%
- C36%
- D20%
Explanation
The coefficient of determination is r² = (−0.8)² = 0.64, so 64% of the variation in one variable is explained by the other. The sign does not affect r². Choosing 80% ignores squaring, and 36% is the unexplained share (1 − 0.64), not the explained share.
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