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CA Foundation · Quantitative Aptitude · Correlation and Regression

A researcher calculates the correlation coefficient between monthly rainfall (in mm) and crop yield (in kg per hectare) for a farming region. The correlation coefficient is found to be +0.92. Which of the following conclusions is most appropriate?

A correlation of +0.92 indicates a very strong positive linear association between rainfall and crop yield. Correlation describes association only; it does not establish causation. The R² value (0.92)² = 0.8464 shows that 84.64% of yield variation is explained by rainfall variation.

  1. ARainfall directly causes crop yield to increase by 92%
  2. BThere is a very strong positive linear relationship; rainfall increase is associated with higher yields, though causation cannot be inferred from correlation aloneCorrect
  3. CExactly 92% of variation in crop yield is explained by rainfall
  4. DRainfall explains 84.64% of the variation in crop yield

Explanation

Correlation of +0.92 shows strong positive association but does not prove causation. Correlation measures linear association, not percentage change. The coefficient of determination (R²) = (0.92)² = 0.8464 or 84.64%, meaning 84.64% of variation in Y is explained by X, not 92%. Option 3 confuses the correlation with R².

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