FRM Part I · FRM Exam Part I · Regression with Multiple Explanatory Variables
In a multiple regression, an analyst finds that the F-test rejects the null that all slope coefficients are zero at the 1% level, yet none of the individual t-statistics on the slope coefficients is significant at the 5% level. Which problem is the most likely explanation?
The most likely cause is multicollinearity. Highly correlated regressors inflate individual standard errors, making each t-statistic insignificant, while together they still explain the dependent variable well, so the joint F-test remains significant. This signature pattern distinguishes it from heteroskedasticity or serial correlation.
- AMulticollinearity among the explanatory variablesCorrect
- BHeteroskedasticity in the error terms
- COmitted variable bias that is uncorrelated with the regressors
- DSerial correlation in a model with no lagged dependent variable
Explanation
Multicollinearity inflates the standard errors of individual coefficients, lowering their t-statistics, while the joint explanatory power of the regressors remains high, so the F-test and R-squared stay significant. Heteroskedasticity and serial correlation mainly distort standard errors in other ways and do not produce this specific pattern.
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