On multivariate discrete least squares

For a positive integer n∈Nn∈N we introduce the index set Nn:={1,2,…,n}Nn:={1,2,…,n}. Let X:={xi:i∈Nn}X:={xi:i∈Nn} be a distinct   set of vectors in RdRd, Y:={yi:i∈Nn}Y:={yi:i∈Nn} a prescribed   data set of real numbers in RR and F:={fj:j∈Nm},m