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

In a multiple regression, each individual coefficient has a t-statistic below the critical value, yet the joint F-test that all slope coefficients are zero is strongly rejected. Which explanation is most consistent with this pattern?

High multicollinearity among the explanatory variables is the likely cause. It inflates individual coefficient standard errors, so each t-statistic is insignificant, while the variables together still explain the dependent variable well, so the joint F-test rejects the hypothesis that all slopes are zero.

  1. AHeteroskedasticity has biased the coefficient estimates
  2. BThe explanatory variables are highly collinear, inflating individual standard errorsCorrect
  3. CThe dependent variable is stationary
  4. DThe sample size is too large relative to the number of variables

Explanation

Multicollinearity raises the standard errors of individual coefficients, lowering their t-statistics, while the variables jointly still explain much of the variation, giving a significant F. Heteroskedasticity affects standard errors but does not typically produce this pattern and does not bias coefficients. A large sample would make t-statistics larger, not smaller.

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