Suppose the same smoother S is used to estimate both terms in a two-term additive model (i.e., both variables are identical). Assume that S is symmetric with eigenvalues in [0, 1). Show that the backfitting residual converges to (I + S) -1 (I - S)y, and that the residual sum of squares converges upward. Can the residual sum of squares converge upward in less structured situations? How does this fit compare to the fit with a single term fit by S?