The approach of subset selection in regression modelling assumes that the chosen fixed full set of predefined basis functions contains a subset that is sufficient to describe the target relation sufficiently well. However, in most cases the necessary set of basis functions is not known and needs to be guessed – a potentially non-trivial (and long) trial and error process. In the paper we consider an adaptive basis function construction approach that in many problems has a potential to be more efficient. It lets the modelling method itself construct the basis functions necessary for creating a regression model of arbitrary complexity with adequate predictive performance. We also introduce an instance of the approach that as a search strategy uses the floating search algorithm. To evaluate the proposed method, we compare it to other regression modelling methods, including the well-known Sequential Forward Selection, on artificial and real world data.