We consider the least squares projection onto the behavior for linear time-invariant (LTI) single-input single-output (SISO) models, in which the observed input-output data are modified in a least squares (LS) sense by subtracting so-called misfits, so that the modified data satisfy a given linear dynamic relation. We show that the LS-criterion of the projection problem induces an orthogonal decomposition of the ambient data space and we characterize this decomposition by means of banded block-Toeplitz matrices, the elements of which are the coefficients of the difference equation describing the SISO LTI dynamics. We thereby generalize earlier results in the literature on autonomous LTI models to the more complicated SISO case. Additionally, we illustrate that the novel characterization is equivalent (up to a change of model representation) to results derived using (isometric) state-space representations in the literature on behavioral systems theory.