FRM Part I · FRM Exam Part I · Linear Regression
In a multiple regression, the estimated slopes are b1 = 0.80 and b2 = 0.30, with standard errors 0.20 and 0.15. The estimated covariance between b1 and b2 is 0.012. What is the t-statistic for H0: β1 = β2?
The t-statistic is about 2.55. The difference in slopes is 0.50, and its variance is 0.04 plus 0.0225 minus twice the covariance of 0.012, which is 0.0385. The standard error is 0.196, so t is 0.50 divided by 0.196.
- A2.00
- B1.70
- C12.99
- D2.55Correct
Explanation
Var(b1 − b2) = 0.04 + 0.0225 − 2(0.012) = 0.0385, so the standard error is 0.1962. t = 0.50/0.1962 = 2.55. Ignoring the covariance gives se = 0.25 and t = 2.00. Adding the covariance instead of subtracting it gives 1.70.
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