CA Foundation · Quantitative Aptitude · Correlation and Regression
For a data set, x̄ = 20, ȳ = 50, σx = 5, σy = 10 and r = 0.8. Using the appropriate regression line, what is the best estimate of X when Y = 60?
The best estimate of X is 24. Estimating X from Y needs the regression of X on Y, whose slope is 0.8 × 5/10 = 0.4. Then X = 20 + 0.4 × (60 − 50) = 24.
- A24Correct
- B28
- C36
- D44
Explanation
To estimate X from Y we use the regression of X on Y. b_xy = r·σx/σy = 0.8 × 5/10 = 0.4. Then X − 20 = 0.4(60 − 50) = 4, so X = 24. The value 36 comes from wrongly using b_yx = 1.6, and 28 from using r = 0.8 as the slope.
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