What does the term 'residuals' refer to in regression analysis?

The term 'residuals' in regression analysis specifically refers to the differences between observed values and the predicted values of the dependent variable. When performing a regression analysis, a model is created to predict the dependent variable based on one or more independent variables. The residual for each observation is calculated by subtracting the predicted value (derived from the regression equation) from the actual observed value. This means that residuals provide valuable insights into how well the model is performing—specifically, they show how far off the predictions are from the actual data points. A smaller residual indicates a better fit for the model, while larger residuals suggest that the model may not be accurately capturing the underlying relationship.

Understanding residuals is crucial for diagnosing the fit of a regression model. Analyzing the pattern and distribution of residuals can help identify issues like heteroscedasticity or non-linearity, which might indicate the need for model adjustments or a re-evaluation of the chosen variables.

The other options address different concepts within regression analysis. The variance of independent variables pertains to the spread or variability of those variables in the dataset, while the predicted values refer to the estimates generated by the regression model that indicate what the dependent variable should be based on observed values of the independent