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CA Foundation · Quantitative Aptitude · Correlation and Regression

A scatter diagram between the age of a machine and its monthly maintenance cost shows points forming a clear U-shaped curve, with costs falling at first and then rising. A student states that r must be strongly negative. What is the best comment on this statement?

The statement is incorrect. Correlation coefficient measures only linear association, and a symmetric U-shaped pattern has falling and rising portions that offset, so r may be close to zero despite a strong non-linear relationship visible in the scatter diagram.

  1. ACorrect, because costs fall at the start
  2. BIncorrect, because r measures only linear relationship, so it may be near zero despite a strong curved relationshipCorrect
  3. CIncorrect, because r must be exactly +1 for a curve
  4. DCorrect, because any visible pattern implies a large negative r

Explanation

Karl Pearson's r measures only the strength of a linear relationship. A symmetric U-shape has a falling and rising part that largely offset, so r can be near zero even though the variables are strongly related. The scatter diagram reveals this non-linearity.

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