What is the main purpose of residual analysis in regression?

Residual analysis in regression serves multiple critical purposes, making the choice of "All of the above" the most comprehensive answer.

First, one of the key uses of residual analysis is to identify outliers in the data. By examining residuals, which are the differences between observed values and predicted values, analysts can spot points that deviate significantly from the model's predictions, thereby highlighting potential outliers.

Second, residual analysis is crucial in confirming the linearity assumption of the regression model. For a linear regression model to be valid, the residuals should be randomly distributed without any discernible patterns. If a pattern appears in the residuals, it suggests that the relationship between the variables might not be properly captured by a linear model, indicating a potential need for a different modeling approach.

Lastly, assessing model fit is another elementary function of residual analysis. By analyzing the size and pattern of the residuals, one can determine how well the model is performing. Ideally, smaller and randomly scattered residuals indicate a better fit, whereas larger residuals may highlight areas where the model fails to predict accurately.

Given these points of analysis—identifying outliers, confirming linearity, and assessing model fit—this multifaceted approach to understanding the residuals makes "All