FRM Part I · FRM Exam Part I · Linear Regression
An analyst runs a simple regression of a bond fund's yield changes on Treasury yield changes and finds R-squared of 0.64. What is the absolute value of the sample correlation between the two variables, and what does the regression imply?
The absolute correlation is 0.80 and 64% of the variation in the fund's yield changes is explained. In simple regression, R-squared equals the squared correlation, so the correlation is the square root of 0.64, while R-squared directly gives the explained share.
- A0.64; 64% of the variation in the fund is explained by the Treasury changes
- B0.80; 64% of the variation in the fund is explained by the Treasury changesCorrect
- C0.80; 80% of the variation in the fund is explained by the Treasury changes
- D0.41; 36% of the variation in the fund is explained by the Treasury changes
Explanation
In a simple regression R-squared equals the squared correlation, so |r| = sqrt(0.64) = 0.80. The explained share of variation is R-squared itself, 64%. Option 3 confuses correlation with explained share.
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