FRM Part I · FRM Exam Part I · Linear Regression
A regression with a large sample gives a slope estimate of 0.85 and a standard error of 0.25. Using a critical value of 1.96, what is the 95% confidence interval for the slope, and what does it imply for testing H0: slope = 0.50 at the 5% level?
The interval is 0.85 plus or minus 1.96 times 0.25, giving 0.36 to 1.34. Since the hypothesized slope of 0.50 lies inside this range, the null hypothesis cannot be rejected at the 5% significance level.
- A0.36 to 1.34; fail to reject H0Correct
- B0.60 to 1.10; reject H0
- C0.36 to 1.34; reject H0
- D0.85 to 1.34; fail to reject H0
Explanation
Margin = 1.96 × 0.25 = 0.49. Interval = 0.85 ± 0.49 = 0.36 to 1.34. The value 0.50 lies inside the interval, so H0 is not rejected. The interval 0.60 to 1.10 wrongly uses a margin of 0.25 (one standard error).
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