In the context of regression, what is a residual?

A residual is defined as the difference between the actual value of a dependent variable and the value predicted by a regression model. In other words, it represents the error of the prediction for a specific observation, indicating how much the predicted value deviates from the actual observed value. This concept is fundamental in regression analysis as it helps to assess the accuracy of the model.

When examining the properties of residuals, they're critical for evaluating the performance of the regression model. Large residuals can indicate that the model does not fit the data well, possibly suggesting the need for model refinement or the consideration of different variables.

The other options present misunderstandings of the concept. For instance, the difference between independent and dependent variables is not indicative of a residual, as residuals are solely concerned with actual versus predicted values. Average distance measures might resemble concepts like the mean absolute error, but they do not capture the individual discrepancies mapped out in residuals. Finally, discussing the sum of errors describes an aggregate approach that doesn't encapsulate the nature of residuals for individual data points. Thus, understanding that a residual is specifically the difference between actual and predicted values is key to effectively analyzing regression outputs.