CA FOUNDATION: QUANTITATIVE APTITUDE · CORRELATION AND REGRESSION

Correlation: sign and coefficient

r = Cov(x, y) ÷ (σx σy). Also r = ±√(byx × bxy), taking the common sign of the regression coefficients.

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Worked examples

Example 1 · level 1

What type of correlation would you expect between: Hours of self-study and marks scored?

  1. Negative
  2. Positive
  3. No correlation
Show solution
  1. Hours of self-study and marks scored: both move in the same direction → Positive.

Answer: Positive

Example 2 · level 2

For two series, Cov(x, y) = 9.6, σx = 4 and σy = 6. Find Karl Pearson’s coefficient of correlation.

Show solution
  1. r = 9.6 ÷ (4 × 6) = 9.6 ÷ 24 = 0.4.

Answer: 0.4

Example 3 · level 3

The regression coefficients are byx = 0.5 and bxy = 0.5. Find the coefficient of correlation r.

Show solution
  1. byx × bxy = 0.25.
  2. √0.25 = 0.5.
  3. Both coefficients are positive, so r = 0.5.

Answer: 0.5

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