# The Difference Between Residual and Error in Statistics

In the field of statistics, the terms “residual” and “error” are often used interchangeably. Many researchers and practitioners consider these terms to have the same meaning, but in reality, they represent significantly different concepts.

Understanding the difference between residuals and errors is crucial for accurate data analysis and proper interpretation of results. Therefore, Kanda Data has written this article to explain the difference between residuals and errors in statistics.

## Difference in Definition: Residual and Error

Residual refers to the difference between the actual observed value and the predicted value from the statistical model used. Residual represents the deviation in the sample data being analyzed. It’s important to emphasize that residuals are used in the context of sample data. Mathematically, the residual can be expressed as:

Residual =  Yi – Ŷi

Where Yi is the actual observed value, and Ŷi is the predicted value from the model.

On the other hand, Error refers to the deviation between the actual observed value and the expected or true value of the target population. The mathematical formula for error is similar to that of residual, but error is used in the context of population data.

Error represents the mistake occurring across the entire population, which cannot always be measured directly. Thus, researchers are expected to understand the distinction between the definitions of residual and error.

## When to Use Residual and Error in Research

Residuals are often used in empirical data analysis where observed sample data is analyzed to evaluate the constructed model. Residuals are used to check whether the statistical model fits the collected data and how well the model can predict outcomes.

In contrast, error is more often associated with theoretical concepts in statistical inference. Error describes the deviation between observed results and the true value of a larger population that cannot be directly observed.

Error is considered a mistake occurring in the entire population, and error analysis helps in understanding how accurate the model estimates are for the population. Therefore, researchers are encouraged to understand when to use residuals and errors in research.

## The Time to Use Residual or Error Correctly

The use of the terms residual or error should be adjusted according to the research context. If you are working with sample data and examining how well your model fits that data, then “residual” is the appropriate term.

Conversely, if you are discussing deviation in the context of a population or making inferences from a sample to a population, then the term “error” is more appropriate.

Using the correct term is not only important for accurate communication but also to ensure that analysis and interpretation of results are done correctly. Misusing these terms can lead to confusion and potential errors in the interpretation of research findings.

## Conclusion

Although residuals and errors are often considered the same in statistics, they have significantly different conceptual meanings. Residual refers to the deviation between observed data and predicted values in a sample, while error refers to the theoretical deviation between observed data and the true value of the population.

Using the correct term in analysis and interpretation is crucial for research accuracy and a better understanding of the phenomena being studied. Understanding the difference between residuals and errors will help researchers conduct more accurate analyses and make more precise interpretations of their results. This is the article Kanda Data has written on this occasion. We hope it is useful to all of you. Stay tuned for more updates from Kanda Data in the future.