CA Foundation · Quantitative Aptitude · Correlation and Regression
Consider these statements about types of correlation. (i) Correlation between the length of a square's side and its area is always perfectly linear. (ii) Zero Pearson correlation between X and Y means no linear relationship, though a non-linear relationship may exist. Which is correct?
Only statement (ii) is correct. Pearson's r measures linear association alone, so zero correlation can coexist with a non-linear relation. Area of a square is the side squared, which is curvilinear, so statement (i) is false.
- ABoth (i) and (ii) are correct
- BOnly (i) is correct
- COnly (ii) is correctCorrect
- DNeither is correct
Explanation
Area equals side squared, so the relationship is curvilinear, not linear. Statement (i) is therefore false. Pearson's r measures only linear association, so r = 0 can coexist with a non-linear relation such as y = x² on symmetric data. Hence (ii) is true.
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