FRM Part I · FRM Exam Part I · Regression with Multiple Explanatory Variables
In a multiple regression of a fund's excess return on three risk factors, a risk analyst finds that the R-squared is high and the overall F-test is highly significant, yet none of the individual slope t-statistics is significant. Which problem is the most likely cause?
The most likely cause is multicollinearity. When explanatory variables are highly correlated, the model fits well overall and the F-test is significant, but individual coefficient standard errors are inflated, so each t-statistic looks insignificant even though the regressors jointly matter.
- AHeteroskedasticity in the residuals
- BSerial correlation in the residuals
- CMulticollinearity among the explanatory variablesCorrect
- DOmitted variable bias from excluding a relevant regressor
Explanation
A high R-squared and significant F-statistic combined with insignificant individual t-statistics is the classic symptom of multicollinearity. Correlated regressors inflate the standard errors of individual coefficients while the joint explanatory power stays high. Heteroskedasticity and serial correlation distort standard errors but do not typically produce this specific pattern.
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