What are the most common errors in regression analysis and how do you fix them?

1 Error 1: Omitting important variables

One of the main assumptions of regression analysis is that the model includes all the relevant variables that affect the outcome. If you omit important variables, you may end up with biased estimates, misleading interpretations, and inaccurate predictions. To avoid this error, you should do a thorough literature review, consult domain experts, and use data visualization and correlation analysis to identify potential predictors. You should also test your model for omitted variable bias using methods such as the Ramsey RESET test, the Hausman test, or the Durbin-Wu-Hausman test.

2 Error 2: Including irrelevant variables

On the other hand, adding too many variables to your model can also cause problems. If you include irrelevant variables, you may reduce the power and efficiency of your model, increase the risk of multicollinearity, and overfit the data. To avoid this error, you should apply the principle of parsimony, which means choosing the simplest model that fits the data well. You should also use model selection criteria such as the Akaike information criterion (AIC), the Bayesian information criterion (BIC), or the adjusted R-squared to compare different models and select the best one.

3 Error 3: Violating the linearity assumption

Another key assumption of regression analysis is that the relationship between the variables is linear, or can be transformed into a linear one. If this assumption is violated, your model may not capture the true nature of the data and produce inaccurate estimates and predictions. To avoid this error, you should check the linearity assumption by plotting the residuals against the predicted values and looking for any patterns or curvature. If you detect any non-linearity, you should try to transform your variables using methods such as logarithms, exponentials, or polynomials.

4 Error 4: Ignoring heteroscedasticity

Heteroscedasticity means that the variance of the error term is not constant across the values of the predictor variables. This can affect the standard errors of your coefficients, leading to unreliable hypothesis tests and confidence intervals. To avoid this error, you should test your model for heteroscedasticity using methods such as the Breusch-Pagan test, the White test, or the Goldfeld-Quandt test. If you find evidence of heteroscedasticity, you should try to correct it by using robust standard errors, weighted least squares, or transforming your variables.

5 Error 5: Overlooking autocorrelation

Autocorrelation means that the error terms are correlated with each other over time or space. This can also affect the standard errors of your coefficients, as well as the R-squared and the Durbin-Watson statistic. To avoid this error, you should test your model for autocorrelation using methods such as the Durbin-Watson test, the Ljung-Box test, or the Breusch-Godfrey test. If you find evidence of autocorrelation, you should try to correct it by using methods such as the Cochrane-Orcutt procedure, the Prais-Winsten procedure, or the Newey-West estimator.

6 Error 6: Misinterpreting the results

The final and perhaps the most crucial error in regression analysis is misinterpreting the results. This can happen if you do not understand the meaning and limitations of the coefficients, the R-squared, the p-values, and the confidence intervals. To avoid this error, you should always check the assumptions and diagnostics of your model, report the results with appropriate caveats and qualifications, and avoid causal claims unless you have a strong theoretical and empirical basis. You should also use common sense and domain knowledge to validate and contextualize your findings.

7 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?