The authors analyse a particularly useful formulation of the scaled total least squares problem. The analysis is based on a new assumption that guarantees existence and uniqueness of meaningful solution for real positive parameters. The proposed in the paper theoretical considerations complex data are allowed. It is shown how any linear system can be reduced to a minimally dimensioned core system satisfying accepted assumption. Consequently, the developed theory and algorithms can be applied to fully general systems. The basics of practical algorithms for solving both scaled total least squares and data least squares problems are indicated for either dense or large sparse systems. All assumptions and their consequences are compared with earlier approaches.