What does the residual sum of squares represent?

The residual sum of squares indeed represents the sum of squared errors, which is a key concept in regression analysis. This measure quantifies the total amount of deviation of the observed values from the values predicted by the model.

When you perform regression, you calculate the difference between each observed value and its corresponding predicted value. These differences are known as residuals. To express how significant these residuals are, you square each one, effectively converting negative differences to positive values and emphasizing larger discrepancies. The residual sum of squares is the total of those squared differences.

This value is critical because it provides insight into the accuracy of the regression model. A lower residual sum of squares indicates that the model's predictions closely align with the actual observed values, while a higher value signifies a poor fit. Therefore, understanding this concept is essential for evaluating the performance of regression models and making improvements to enhance their predictive capability.