FRM Part I · FRM Exam Part I · Linear Regression
In a multiple regression with two explanatory variables, the estimated slopes are b1 = 0.80 and b2 = 0.50. The standard errors are 0.20 and 0.15, and the estimated covariance between b1 and b2 is 0.012. What is the t-statistic for testing H0: β1 = β2?
The t-statistic is 1.53. The difference in slopes is 0.30. Its variance is 0.04 + 0.0225 − 2×0.012 = 0.0385, giving a standard error of about 0.196. Dividing 0.30 by 0.196 gives 1.53, which is below the usual 5% critical value.
- A1.53Correct
- B1.20
- C1.02
- D7.79
Explanation
Var(b1 − b2) = 0.04 + 0.0225 − 2(0.012) = 0.0385, so the standard error is 0.1962. t = 0.30/0.1962 = 1.53. Ignoring the covariance gives 0.30/0.25 = 1.20. Adding the covariance gives 0.30/0.2941 = 1.02. Dividing by the variance rather than the standard error gives 7.79.
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