FRM Part I · FRM Exam Part I · Linear Regression
A regression of a bond's yield change (Y, in basis points) on a benchmark yield change (X, in basis points) gives fitted Y = 0.5 + 0.80X. The sample standard deviation of X is 6 bp and of Y is 8 bp. What is the sample correlation between X and Y?
The correlation is 0.60. In simple regression the slope equals the correlation times the ratio of the standard deviation of Y to that of X. Rearranging gives 0.80 times 6 divided by 8, which equals 0.60.
- A0.60Correct
- B0.80
- C1.07
- D0.75
Explanation
In simple regression slope = correlation x (sd Y / sd X). So correlation = slope x sd X / sd Y = 0.80 x 6/8 = 0.60. Using 0.80 confuses slope with correlation; 1.07 inverts the ratio (0.80 x 8/6), which is impossible as correlation cannot exceed 1.
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