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CA Foundation · Quantitative Aptitude · Correlation and Regression

A scatter diagram of Y against X shows points forming a clear U-shaped curve, symmetric about the vertical line through the mean of X. Which conclusion about the Karl Pearson coefficient r is most appropriate?

r will be close to zero even though the variables are strongly related. Pearson's coefficient measures only linear association, and in a symmetric U-shaped pattern the upward and downward halves cancel each other, so covariance is almost zero.

  1. Ar will be close to +1 because the relationship is strong
  2. Br will be close to -1 because the curve falls first
  3. Cr will be close to zero even though the variables are strongly relatedCorrect
  4. Dr cannot be computed because the diagram is not a straight line

Explanation

Pearson's r measures only linear association. In a symmetric U-shape, the rising and falling halves cancel in the covariance, so r is near zero despite a strong non-linear relationship. The formula can still be computed, so option 4 is wrong.

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