What does the term 'residuals' refer to in a regression context?

In the context of regression analysis, 'residuals' denote the difference between the observed values (the actual data points) and the predicted values derived from the regression model. Specifically, for each data point, the residual quantifies how far off the predicted value is from the actual measurement. This concept is essential as it helps to assess the model's accuracy; smaller residuals indicate a better fit of the model to the data, while larger residuals suggest that the model may not be representing the underlying relationship effectively.

Analyzing residuals allows statisticians to identify patterns, check the assumptions of regression, and potentially guide improvements in model fitting. This understanding of the residuals is crucial for interpreting the performance of the regression model and ensuring reliable predictions.