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

In a multiple regression, an analyst finds that each individual t-statistic on two highly correlated explanatory variables is below 1.0, yet the joint F-test on the regression is highly significant with a very small p-value. Which is the most likely explanation?

The pattern is the classic symptom of multicollinearity: correlated regressors inflate individual standard errors, so each t-statistic is small, while the F-test shows the variables are jointly significant in explaining the dependent variable.

  1. AHeteroskedasticity has made the F-statistic invalid, so the t-statistics should be trusted
  2. BMulticollinearity has inflated the standard errors of the individual coefficients while the variables jointly explain the dependent variableCorrect
  3. CThe model has too many observations, which makes t-statistics unreliable
  4. DThe intercept is omitted, which biases the F-test only

Explanation

High correlation between regressors inflates coefficient standard errors, lowering individual t-statistics, while the joint F-test still detects their combined explanatory power. The other options do not generate this specific pattern.

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