FRM Part I · FRM Exam Part I · Regression with Multiple Explanatory Variables
In a multiple regression of fund returns on four factor exposures, none of the individual slope t-statistics is significant at the 5% level, yet the F-test of the hypothesis that all four slopes are zero is strongly rejected. Which explanation is most consistent with this result?
The pattern of insignificant individual t-statistics with a significant joint F-test is typical of multicollinearity. Highly correlated regressors inflate the individual standard errors, hiding each variable's separate effect, but together they still explain a significant share of the variation in the dependent variable.
- AThe explanatory variables are highly correlated with each other, inflating individual standard errors while jointly explaining the dependent variableCorrect
- BThe error terms are serially uncorrelated, which makes the individual t-tests invalid
- CThe R-squared of the regression is close to zero
- DThe regression has omitted the intercept, which invalidates the F-test only
Explanation
Multicollinearity inflates the standard errors of the individual coefficients, so each t-statistic is small. The regressors still have joint explanatory power, so the F-test rejects. A near-zero R-squared would not lead to a strong F rejection. Serially uncorrelated errors are a standard assumption and do not invalidate t-tests.
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