Least squares is a method of adjusting observations in which the sum of the squares of which quantity is minimized?

• A. Denominators
• B. Numerators
• C. Weights
• D. Residuals

Answer: (D)

Least squares fits a model by making the differences between observed values and model predictions as small as possible when those differences are squared and summed. Those differences are called residuals. The method minimizes the total squared residuals, which prevents positive and negative errors from canceling out and places more emphasis on larger errors. In the standard formulation, the objective is the sum of squared residuals; denominators, numerators, or weights aren’t what’s being minimized (weights would only come in a generalized, weighted version).