CA Foundation · Quantitative Aptitude · Correlation and Regression
A sample of 25 pairs of observations gives r = 0.6. Using the formula PE = 0.6745 × (1 - r²)/√n, what is the probable error of the coefficient of correlation (rounded to four decimals)?
The probable error is 0.0863. With r = 0.6, 1 - r² is 0.64, and the square root of 25 is 5. So PE = 0.6745 × 0.64 / 5 = 0.0863. Using 1 - r instead of 1 - r² would be incorrect.
- A0.0863Correct
- B0.0540
- C0.0173
- D0.1079
Explanation
1 - r² = 1 - 0.36 = 0.64 and √25 = 5. PE = 0.6745 × 0.64 / 5 = 0.4317/5 = 0.0863. Using (1 - r) = 0.4 instead of 1 - r² gives 0.0540, which is wrong.
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