CA Foundation · Quantitative Aptitude · Correlation and Regression
For a bivariate data set, x̄ = 40, ȳ = 60, σx = 5, σy = 10 and r = 0.8. Using the regression line of x on y, what is the estimated value of x when y = 70?
The estimated x is 44. The regression coefficient of x on y is 0.8 × 5/10 = 0.4. Then x = 40 + 0.4 × (70 − 60) = 44. The x-on-y line must be used, not the y-on-x line.
- A44Correct
- B56
- C28
- D72
Explanation
bxy = r·σx/σy = 0.8 × 5/10 = 0.4. The line is x − 40 = 0.4(y − 60), so at y = 70, x = 40 + 0.4 × 10 = 44. The value 56 comes from using byx = 1.6 instead of bxy. The value 72 comes from swapping the two means.
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