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CA Foundation · Quantitative Aptitude · Correlation and Regression

Consider the following statements about Karl Pearson's coefficient of correlation r. I. If r = 0, then x and y must be independent of each other in every possible way. II. r is independent of change of origin and scale (for positive scale factors). III. r measures the strength of linear relationship only. Which statements are correct?

Only statements II and III are correct. Zero correlation implies no linear relationship, not independence, since a nonlinear dependence such as y = x² can give r = 0. The coefficient is unaffected by change of origin and scale and measures linear association only.

  1. AI and II only
  2. BII and III onlyCorrect
  3. CI and III only
  4. DI, II and III

Explanation

Statement I is false: r = 0 only means no linear relationship; for example y = x² over values symmetric about zero gives r = 0 although y depends on x completely. Statement II is true as r is unaffected by shifting origin or dividing by positive constants. Statement III is true since r captures linear association only. So II and III are correct.

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