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

A researcher estimates a regression of bond spread changes on three variables using 83 observations. The coefficient on variable X1 is 0.90 with standard error 0.30, and the coefficient on X3 is -0.50 with standard error 0.40. Each has a two-sided 5% critical value of about 1.99. Which conclusion is correct?

X1 has t = 0.90/0.30 = 3.00, above the 1.99 critical value, so it is significant. X3 has t = -0.50/0.40 = -1.25, whose absolute value is below 1.99, so it is not significant. Only X1 is significant at the 5% level.

  1. ABoth coefficients are significant at 5%
  2. BNeither coefficient is significant at 5%
  3. CX1 is significant at 5% but X3 is notCorrect
  4. DX3 is significant at 5% but X1 is not

Explanation

t for X1 = 0.90/0.30 = 3.00, which exceeds 1.99, so reject zero. t for X3 = -0.50/0.40 = -1.25, with absolute value below 1.99, so do not reject. Treating the negative sign as lowering significance is a mistake; only the absolute value matters.

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