Which statement about the composition of the sum of squares is true?

Which statement about the composition of the sum of squares is true?

• A. SS is the sum of the squares of the raw data
• B. SS equals the sum of squared residuals
• C. SS is the sum of squared deviances
• D. SS equals the square of the sum of the deviations

Answer: (C)

In this context, sum of squares is interpreted through the lens of how far the model’s predictions are from what is observed, measured on a likelihood scale rather than by plain squared deviations. In generalized linear models, the natural measure of lack of fit is the deviance, and the total deviance is decomposed into model (explained) deviance and residual (unexplained) deviance, just like SST decomposes into SSR and SSE in ordinary least squares. So the sum of squares can be described as the sum of squared deviances because that is the way variability is quantified when using deviance-based fits. The other options don’t fit this framework: using raw data squares isn’t how SS is defined in modeling, the sum of squared residuals corresponds to SSE rather than the overall SS in this setting, and squaring the sum of deviations isn’t a meaningful measure of variability (the sum of deviations from the reference value is zero, making its square meaningless for SS).

In this context, sum of squares is interpreted through the lens of how far the model’s predictions are from what is observed, measured on a likelihood scale rather than by plain squared deviations. In generalized linear models, the natural measure of lack of fit is the deviance, and the total deviance is decomposed into model (explained) deviance and residual (unexplained) deviance, just like SST decomposes into SSR and SSE in ordinary least squares. So the sum of squares can be described as the sum of squared deviances because that is the way variability is quantified when using deviance-based fits. The other options don’t fit this framework: using raw data squares isn’t how SS is defined in modeling, the sum of squared residuals corresponds to SSE rather than the overall SS in this setting, and squaring the sum of deviations isn’t a meaningful measure of variability (the sum of deviations from the reference value is zero, making its square meaningless for SS).