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CA Foundation · Quantitative Aptitude · Correlation and Regression

Which of the following statements about Karl Pearson's coefficient of correlation (r) is correct?

Karl Pearson's coefficient is a unit-free number lying between -1 and +1 inclusive. Covariance is divided by the product of the standard deviations, so the units cancel. A change of origin, such as adding a constant, leaves r unchanged.

  1. AIt is a pure number that always lies between -1 and +1, both inclusiveCorrect
  2. BIt is expressed in the product of the units of X and Y
  3. CIt can take any value between 0 and 2
  4. DIt changes in value when a constant is added to every observation of X

Explanation

Since the covariance is divided by the product of the two standard deviations, the units cancel and r is a pure number. By the Cauchy-Schwarz inequality it lies within -1 and +1. Adding a constant to every X value is a change of origin, which does not alter r, so the last option is wrong.

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