Component sums of squares for the factor model

The three components of the total sum of squares reflect different aspects of the data set.

Describes how much linear trend is in the data.
Describes how much curvature is in the data.
Describes the variation within each group — the unexplained variation.

In particular, the nonlinear sum of squares holds information about the curvature in the data.

Illustration

The scatterplot on the left below shows an artificial data set. The jittered dot plots on the right show the different components — click on any plot to display these components on the scatterplot.

The two sliders alter the data set, keeping the total sum of squares unchanged.

'Variation' slider
This adjusts how close the data points lie to a quadratic curve. Observe that the residual sum of squares is smallest when the relationship is strongest.
'Curvature' slider
This slider adjusts the amount of curvature in the data. It therefore alters the distance between the least squares straight line and the group means. Observe how that the relative size of the linear and nonlinear sums of squares change.