The sum of squares (SS) is an estimate of what?

• A. The mean
• B. Total variability around a parameter
• C. Cross-products among variables
• D. The residual variance

Answer: (B)

Sum of squares quantifies how much the data vary around a central value. It sums up the squared deviations of each observation from a reference point, usually the grand mean, so larger SS means more spread in the data. This makes SS an estimate of variability in the population: after dividing by the appropriate degrees of freedom, you get an estimate of the variance. In analysis of variance and regression, you partition this total variability into components (explained by the model and unexplained residual). The residual variance, however, comes from the mean square for error (SSE divided by its degrees of freedom), not from the total sum of squares itself. The mean is a measure of central tendency, not variability, and cross-products among variables relate to covariances, not the sum of squares as a measure of dispersion.