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CA Foundation · Quantitative Aptitude · Correlation and Regression

Which statement about the Karl Pearson coefficient of correlation is correct?

Karl Pearson's coefficient is independent of change of origin and scale, provided the scale factors are positive. It is a unit-free number that measures only the strength and direction of linear association, and its sign depends on how the variables move together, not on their units.

  1. AIt is independent of change of origin and scale (with positive scale factors)Correct
  2. BIt measures non-linear relationships as accurately as linear ones
  3. CIt is expressed in the units of the product of the two variables
  4. DIt is always positive if both variables are measured in the same units

Explanation

Adding or subtracting a constant, or multiplying or dividing by a positive constant, does not change r. It is a pure number without units and measures only linear association. Using the same units does not decide its sign.

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