What represents the relationship between predicted values and the average of input values?

The relationship between predicted values and the average of input values is best represented by the regression sum of squares. This metric is part of the overall analysis of variance in regression analysis, indicating how well the predicted values from a regression model correspond to the actual data points.

Regression sum of squares measures the variation explained by the independent variables in the model. It quantifies the portion of the total variation in the dependent variable that can be attributed to the independent variables. In essence, it captures how much the predicted values deviate from the mean of the actual values, thereby reflecting the strength and effectiveness of the predictive model. By comparing the predicted outcomes to the average of the input values, it demonstrates the model’s validity and capacity to explain the variability of the dependent variable.

In contrast, mean absolute error evaluates the average magnitude of errors in a set of predictions, without considering their direction, and does not specifically reflect the relationship to the input averages. Residual sum of squares focuses on the discrepancies between observed and predicted values, but it does not directly relate to the means of the inputs. Variance analysis is a broader statistical technique used to assess the differences between groups, which does not specifically pertain to the predicted values and input averages in regression modeling.