Which criterion computes the sum of squared residuals between observed and predicted values?

Which criterion computes the sum of squared residuals between observed and predicted values?

• A. Nonlinear Least Squares (NLS)
• B. Dynamic Learning Rate
• C. Batch Gradient Descent
• D. Residual Sum of Squares (RSS)

Answer: (D)

Sum of squared residuals is the standard way to quantify how well a regression model fits the data. For each observation, you take the difference between what you actually observe and what the model predicts, square that difference to keep all errors positive and to emphasize larger mistakes, and then add all those squared differences together. The resulting Residual Sum of Squares tells you how far off the predictions are overall—the smaller, the closer the model is to the data. In ordinary least squares, this sum is the objective we minimize to find the best-fitting parameters, so RSS becomes the primary criterion for fit. Nonlinear Least Squares is a fitting approach used when the relationship between variables is nonlinear in the parameters; it often aims to minimize the same RSS, but it’s a method, not the criterion itself. Batch Gradient Descent is an optimization algorithm that updates parameters to reduce a loss like RSS, rather than the measure of fit itself. Dynamic Learning Rate is a technique for adjusting the step size during optimization, not a criterion for evaluating model fit.

Sum of squared residuals is the standard way to quantify how well a regression model fits the data. For each observation, you take the difference between what you actually observe and what the model predicts, square that difference to keep all errors positive and to emphasize larger mistakes, and then add all those squared differences together. The resulting Residual Sum of Squares tells you how far off the predictions are overall—the smaller, the closer the model is to the data. In ordinary least squares, this sum is the objective we minimize to find the best-fitting parameters, so RSS becomes the primary criterion for fit.

Nonlinear Least Squares is a fitting approach used when the relationship between variables is nonlinear in the parameters; it often aims to minimize the same RSS, but it’s a method, not the criterion itself. Batch Gradient Descent is an optimization algorithm that updates parameters to reduce a loss like RSS, rather than the measure of fit itself. Dynamic Learning Rate is a technique for adjusting the step size during optimization, not a criterion for evaluating model fit.