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

For 25 paired observations of monthly income and expenditure of households in Jaipur, r = 0.6. Using PE = 0.6745 x (1 - r²)/√n, the probable error of r is approximately:

The probable error is about 0.0863. With r equal to 0.6 and n equal to 25, one minus r squared is 0.64, and dividing by the square root of 25, which is 5, gives 0.128. Multiplying by 0.6745 yields roughly 0.0863.

  1. A0.0863Correct
  2. B0.1280
  3. C0.0540
  4. D0.0173

Explanation

1 - r² = 1 - 0.36 = 0.64 and √25 = 5, so 0.64/5 = 0.128. Multiplying by 0.6745 gives about 0.0863. 0.128 omits the factor 0.6745, 0.0540 uses (1 - r) instead of (1 - r²), and 0.0173 divides by n instead of √n.

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