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FRM Part I · FRM Exam Part I · Regression Diagnostics

A risk analyst estimates a regression and finds R² = 0.64 with a significant F-statistic, yet each of two highly correlated regressors has an insignificant t-statistic. Deleting a single influential outlier changes one coefficient from 0.80 to 0.35. Which diagnosis best fits both findings?

The pattern points to multicollinearity, which inflates standard errors and makes individual t-statistics insignificant despite a high R² and significant F, plus an influential observation that shifts a coefficient substantially. Perfect collinearity would prevent estimation, and heteroskedasticity does not bias coefficients.

  1. AHeteroskedasticity alone, because it biases the coefficients
  2. BMulticollinearity among the regressors together with an influential observation affecting the estimatesCorrect
  3. COmitted variable bias eliminated by the outlier
  4. DPerfect multicollinearity, because R² is high

Explanation

High R² and significant F with insignificant individual t-statistics on correlated regressors is the classic sign of multicollinearity, which inflates standard errors. The large coefficient change after deleting one point indicates an influential observation. Perfect multicollinearity would prevent estimation, and heteroskedasticity does not bias coefficients.

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