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FRM Part I · FRM Exam Part I · Regression Diagnostics

In a multiple regression of monthly fund returns on four explanatory variables, an analyst finds that the R-squared is high and the F-test is highly significant, yet none of the individual slope t-statistics is significant at the 5% level. Which problem is the most likely cause?

Multicollinearity is the most likely cause. When explanatory variables are highly correlated, standard errors of individual coefficients rise, so t-statistics become insignificant, while the regressors jointly still explain much of the variance, giving a high R-squared and a significant F-test.

  1. AHeteroskedasticity in the residuals
  2. BMulticollinearity among the explanatory variablesCorrect
  3. COmitted variable bias from a missing regressor
  4. DSerial correlation in the residuals

Explanation

A high joint significance with insignificant individual coefficients is the classic symptom of multicollinearity. Correlated regressors inflate standard errors of individual slopes, lowering t-statistics, while together they still explain much of the variation in the dependent variable. Heteroskedasticity and autocorrelation affect standard errors but do not produce this specific pattern.

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