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FRM Part I · FRM Exam Part I · Regression with Multiple Explanatory Variables

In a multiple regression with 124 observations and 4 explanatory variables, the estimated coefficient on variable X2 is 1.80 with a standard error of 0.75. Using a critical value of 1.98 for a two-sided 95% interval, which interval is the 95% confidence interval for the true coefficient?

A 95% confidence interval is the estimate plus or minus the critical value times the standard error. Here 1.98 × 0.75 = 1.485, so the interval is 1.80 ± 1.485, or 0.3150 to 3.2850. Because zero lies outside it, the coefficient is significant at 5%.

  1. A0.3150 to 3.2850Correct
  2. B0.33 to 3.27
  3. C0.0600 to 3.5400
  4. D1.05 to 2.55

Explanation

The interval is 1.80 ± 1.98 × 0.75 = 1.80 ± 1.485, giving 0.315 to 3.285. The 0.33 to 3.27 option uses 1.96 (z-value) instead of the supplied critical value. The 1.05 to 2.55 option uses only one standard error, and the 0.06 to 3.54 option uses a multiplier of about 2.32.

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