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CA Foundation · Quantitative Aptitude · Correlation and Regression

For the data x: 1, 2, 3, 4, 5 and y: 1, 4, 9, 16, 25 (y = x²), the Pearson correlation coefficient is approximately 0.98. Which conclusion is correct?

The coefficient is high although the relationship is non-linear, so r alone does not reveal the form of the relation. r equals 1 only for an exact linear relation, and y = x² is curved, which gives about 0.98.

  1. AThe relationship is exactly linear because r is close to 1
  2. Br is high even though the relationship is non-linear, so r alone does not show the form of the relationCorrect
  3. Cr must be exactly 1 because y is a perfect function of x
  4. DThe variables are weakly correlated because y is not a linear function of x

Explanation

y is an exact but curved function of x, yet over this range the points lie close to a straight line, giving r near 0.98. A perfect functional relation does not imply r = 1, which needs an exact linear relation, so C is wrong. A is wrong because r is not exactly 1 and the relation is not linear. D ignores the high value of r.

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