FRM Part I · FRM Exam Part I · Linear Regression
An analyst regresses a bond portfolio's yield change on changes in a benchmark yield using 42 observations. The estimated slope is 0.80 with a standard error of 0.25. The two-sided 95% critical t-value with 40 degrees of freedom is 2.02. What is the 95% confidence interval for the slope?
The 95% confidence interval is 0.295 to 1.305. With 40 degrees of freedom the critical value is 2.02, so the margin of error is 2.02 times 0.25, which is 0.505, added to and subtracted from the slope estimate of 0.80.
- A0.295 to 1.305Correct
- B0.55 to 1.05
- C-0.295 to 1.305
- D0.31 to 1.29
Explanation
Margin = 2.02 x 0.25 = 0.505. Interval = 0.80 ± 0.505 = 0.295 to 1.305. The 0.55 to 1.05 option uses only one standard error. The 0.31 to 1.29 option uses 1.96 (about 0.49), ignoring the t-distribution.
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