FRM Part I · FRM Exam Part I · Regression Diagnostics
In a multiple regression of a fund's excess return on several factor returns, an analyst finds that the R-squared is high and the F-test is highly significant, yet none of the individual slope coefficients has a significant t-statistic. Which problem is the most likely cause?
The most likely cause is multicollinearity. When explanatory variables are highly correlated, the model can fit well and pass the joint F-test, but individual coefficient standard errors are inflated, so each t-statistic is insignificant. The other problems do not produce this characteristic pattern.
- AHeteroskedasticity of the residuals
- BMulticollinearity among the explanatory variablesCorrect
- CSerial correlation of the residuals
- DOmission of a relevant variable that is uncorrelated with the included regressors
Explanation
High joint explanatory power with insignificant individual coefficients is the classic symptom of multicollinearity: correlated regressors inflate standard errors of individual slopes while the model fits well overall. Heteroskedasticity and serial correlation mainly distort standard errors without this specific pattern. Omitting an uncorrelated variable does not inflate the standard errors in this way.
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