FRM Part I · FRM Exam Part I · Linear Regression
In a regression of 27 observations, the estimated slope is 0.60 and the test of H0: slope = 0 gives a t-statistic of 2.50. The two-sided 5% critical t-value with 25 degrees of freedom is 2.06. What is the 95% confidence interval for the slope, and is zero inside it?
The standard error is 0.60 divided by 2.50, or 0.24. Multiplying by 2.06 gives a margin of about 0.49, so the interval is roughly 0.11 to 1.09. Zero lies outside it, consistent with rejecting the null of no relationship.
- A0.0 to 1.20 roughly, specifically 0.0 to 1.20 including zero
- B0.085 to 1.115; zero is outsideCorrect
- C0.60 to 1.115; zero is outside
- D0.085 to 1.115; zero is inside
Explanation
SE = 0.60/2.50 = 0.24. Margin = 2.06 × 0.24 = 0.4944. Interval = 0.6 ± 0.4944 = 0.106 to 1.094. Rounded, this is about 0.11 to 1.09, and zero is outside, consistent with t = 2.50 > 2.06. Option 2 is the closest, and it correctly concludes that zero lies outside.
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