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SCIENCE

The Claim

In a linear regression model, correlation between two predictor variables can be accommodated by the model without necessarily causing a problem.

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The Short Version

The claim is well supported. Correlated predictors do not automatically violate linear regression assumptions or make OLS estimates biased, and many models handle moderate correlation without serious practical difficulty. The real concern is severe or near-perfect multicollinearity, which can inflate standard errors and make individual coefficients unstable, especially for inference.

Caveats

  • This does not mean correlated predictors are never a problem; severe or perfect multicollinearity can make coefficients unstable or unidentified.
  • Whether correlation is acceptable depends on the goal: prediction may remain strong even when coefficient interpretation becomes weak.
  • Heuristic cutoffs such as VIF thresholds are context-dependent and should not be treated as universal proof that multicollinearity is or is not a problem.

The Receipts

  1. Regression with Highly Correlated Predictors: Variable Selection and Model Estimation

    PMC

  2. Multicollinearity in Regression Analyses Conducted in Epidemiology

    PubMed Central

  3. Evaluation of Variance Inflation Factors in Regression Models in the Presence of Heteroscedasticity

    National Library of Medicine (PMC)

  4. Omitted-variable bias

    Wikipedia

  5. Multicollinearity and misleading statistical results

    PubMed Central

  6. Tutorial 2 - OLS Bias & Regression Analysis Solutions

    Studocu

  7. Multicollinearity

    StatLect

  8. Variance inflation factor

    Wikipedia

  9. Section 11 Endogenous Regressors and Instrumental ...

    Reed College Economics

  10. 6.5: Multicollinearity

    Statistics LibreTexts

+ 27 more sources — see the full list on Lenz

Filed Under

Linear RegressionMulticollinearityOrdinary Least Squares