CA Foundation · Quantitative Aptitude · Correlation and Regression
For a sample of firms, the mean of x is 40 and the mean of y is 60. The standard deviations are σx = 10 and σy = 8, and r = 0.6. Using the regression line of y on x, what is the estimated value of y when x = 50?
The estimate is 64.8. The regression coefficient of y on x is 0.6 × 8/10 = 0.48, so y = 60 + 0.48 × (50 − 40) = 64.8. Using the x-on-y coefficient 0.75 would wrongly give 67.5.
- A64.8Correct
- B67.5
- C24.0
- D84.0
Explanation
b_yx = 0.6 × 8/10 = 0.48. The line is y − 60 = 0.48(x − 40), so at x = 50, y = 60 + 0.48 × 10 = 64.8. The value 67.5 results from using b_xy = 0.75 (the wrong regression coefficient).
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