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CFA Level I · CFA Level I Exam · Applications of Simple Linear Regression in Finance

In a simple linear regression of a bond fund's returns on changes in yields, the F-test of the slope is highly significant, but R-squared is only 0.12. The most appropriate interpretation is that the yield variable:

The yield variable has a statistically significant relationship with returns but explains little of their variation. The significant F-test rejects a zero slope, while an R-squared of 0.12 means only 12 percent of return variability is explained, so the two measures answer different questions.

  1. Ahas a statistically significant relationship with returns but explains little of their variationCorrect
  2. Bhas no statistically significant relationship with returns because R-squared is low
  3. Cexplains most of the variation in returns because the F-statistic is large

Explanation

A significant F-test shows the slope differs from zero, while R-squared of 0.12 shows only 12% of return variation is explained. The two measure different things, so a low R-squared does not negate significance, and significance does not imply high explanatory power.

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