Residual Analysis

Definition

Residual analysis is a statistical technique used to evaluate the goodness-of-fit of a regression model by examining the residuals, which are the differences between observed and predicted values. This method helps to identify any patterns in the residuals that may indicate problems with the model, such as non-linearity or heteroscedasticity, and is essential for ensuring valid conclusions in impact estimation.

5 Must Know Facts For Your Next Test

1. Residual analysis helps to check if the assumptions of linear regression are met, such as linearity, independence, and normality of residuals.
2. Patterns in residual plots can indicate whether additional variables should be included in the model or if a different modeling approach is needed.
3. A common practice in residual analysis is to create scatter plots of residuals versus predicted values to visually assess any trends or patterns.
4. If residuals show a funnel shape when plotted, it suggests heteroscedasticity, indicating that the model may need adjustments to account for changing variance.
5. Residual analysis is crucial for diagnosing potential issues in regression models that can lead to incorrect conclusions about causal relationships in impact evaluation.

Review Questions

• How does residual analysis contribute to verifying the assumptions of a regression model?
  • Residual analysis plays a vital role in verifying the assumptions of a regression model by examining the residuals for patterns that indicate violations. For instance, if the residuals show a systematic pattern when plotted against predicted values, it suggests non-linearity or that key variables might be missing. By identifying these issues, analysts can improve model fit and enhance the validity of impact estimation.
• Discuss how heteroscedasticity can affect regression results and how residual analysis can help identify it.
  • Heteroscedasticity can significantly distort regression results by leading to inefficient estimates and biased standard errors, which affect hypothesis testing. Residual analysis aids in identifying this issue through visual methods such as plotting residuals against fitted values. If a clear pattern emerges indicating varying spread across different levels of an independent variable, it signals that adjustments may be needed to correct for heteroscedasticity.
• Evaluate the importance of residual analysis in ensuring accurate impact estimation and decision-making.
  • Residual analysis is crucial for ensuring accurate impact estimation because it directly influences how we interpret the relationships within data. By diagnosing potential issues like model mis-specification or violations of regression assumptions, analysts can make informed adjustments to improve model validity. This careful evaluation leads to more reliable insights and ultimately better decision-making based on the estimated impacts of interventions or policies.

Related terms

Residuals: Residuals are the differences between the observed values of the dependent variable and the values predicted by a regression model.

Heteroscedasticity: Heteroscedasticity refers to a situation in regression analysis where the variance of the residuals is not constant across all levels of the independent variable.

Model Specification: Model specification involves selecting the appropriate functional form and variables for a regression model to accurately capture the relationship being studied.