This paper is about nonparametric regression function estimation, first in the independent setting and in a second stage, in the context of an autoregressive model or of discrete time observation of a diffusion process, both settings corresponding to dependent variables. Our estimator is a one step projection estimator obtained by least-squares contrast minimization. The specificity of our work is to consider a new model selection procedure including a cutoff for the underlying matrix inversion, and to provide theoretical risk bounds that apply to non compactly supported bases, a case which was specifically excluded of all previous results. Upper and lower bounds for new rates are provided.