Relationships between Linear Statistical Models

To study the relationship between the linear statistical models we used methods of linear algebra, Hilbert spaces and statistics. It was found that there is a linear relationship between linear statistical models which is expressed by a matrix equality. Several corollaries are derived and discussed, and a new interpretation is proposed for the parameters of linear statistical model. The given relation between the linear statistical models may be useful for both theoretical analysis of statistical models and interpretation of applied statistical models, in particular, to analyze the impact of confounders.