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What is residual analysis?

Residual analysis is a statistical procedure applied in various disciplines such as statistics, econometrics, and natural sciences. It is used to analyze the differences between observed values and predicted values in a statistical model.

Purpose of Residual Analysis

Residuals are the differences between observed values and predicted values in a model. Analyzing these residuals helps evaluate the quality and validity of the model. The main objectives of residual analysis are:

• Identifying Patterns: Residuals assist in identifying patterns or systematic errors in the model. This can indicate missing variables, non-linearities, or other modeling issues.
• Checking Assumptions: Many statistical models have assumptions like normal distribution of residuals. Residual analysis helps check these assumptions and ensure the model is appropriate.
• Detecting Outliers: Residuals can indicate outliers that may have a significant impact on modeling. Detecting and addressing outliers is important for creating robust models.

Conducting Residual Analysis

Residual analysis typically involves calculating residuals, creating plots, and performing statistical tests. Common methods include the residual plot, QQ-plot (Quantile-Quantile plot), and the Shapiro-Wilk test to check the normality of residuals.

It's important to note that careful residual analysis is necessary to ensure model assumptions are met and the model provides reliable predictions.

Conclusion

Residual analysis is an indispensable tool in statistical modeling. It helps improve models, identify patterns, and ensure model assumptions are met. Through thorough residual analysis, researchers and analysts can ensure their models are accurate and reliable.