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FRM Part II · FRM Exam Part II · Correlation Basics: Definitions, Applications, and Terminology

Two variables have the following five paired observations: X = 1, 2, 3, 4, 5 and Y = 1, 4, 9, 16, 25. What is the Spearman rank correlation, and how does it compare with the Pearson correlation?

Spearman is exactly 1.0 and Pearson is below 1.0. Y rises strictly with X, so the ranks match perfectly. The relationship is quadratic rather than linear, so Pearson is high, about 0.98, but not perfect.

  1. ASpearman is 1.0; Pearson is below 1.0Correct
  2. BSpearman is below 1.0; Pearson is 1.0
  3. CSpearman is 1.0; Pearson is also exactly 1.0
  4. DSpearman is 0.0; Pearson is above 0.9

Explanation

Y increases strictly with X, so the ranks are identical (1 to 5) and the rank correlation is exactly 1. The relationship is convex, not linear, so Pearson is high (about 0.98) but below 1. Option C wrongly assumes a monotonic relationship is linear.

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