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CMA Foundation · Fundamentals of Business Mathematics and Statistics · Correlation and Regression

From 100 pairs of observations on the monthly income and spending of households in Jaipur, r = 0.8. Using PE = 0.6745 × (1 − r²)/√n, the probable error of r is approximately:

The probable error is 0.6745 times (1 minus r squared) divided by the square root of n. With r = 0.8 and n = 100 this is 0.6745 × 0.36 / 10, which is about 0.0243.

  1. A0.0243Correct
  2. B0.0360
  3. C0.0135
  4. D0.0024

Explanation

1 − r² = 1 − 0.64 = 0.36 and √100 = 10, so the standard error is 0.036. Multiplying by 0.6745 gives 0.02428, which is about 0.0243. The value 0.0360 is wrong because it omits the 0.6745 factor.

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