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CA Foundation · Quantitative Aptitude · Correlation and Regression

Which of the following statements about the Karl Pearson coefficient of correlation r is correct?

Karl Pearson's r is independent of change of origin and scale, provided the scale constants are positive. It is a unit-free number between -1 and +1 and measures only the strength of linear association, so the other statements about range, units and nonlinearity are incorrect.

  1. AIt measures nonlinear relationships as accurately as linear ones
  2. BIt is independent of the change of origin and scale (for positive scale constants)Correct
  3. CIt can take any value between -2 and +2
  4. DIt is expressed in the units of the product of the two variables

Explanation

r is a pure number lying between -1 and +1 and measures only linear association. Adding or subtracting constants, or multiplying by positive constants, leaves it unchanged. The other options contradict these properties.

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