Life cycle assessment (LCA) is a method used to quantify the environmental impacts of a product, process, or service across its whole life cycle. One of the problems occurring when the system at hand involves processes delivering more than one valuable output is the apportionment of resource consumption and environmental burdens in the correct proportion amongst the products. The mathematical formulation of the problem is represented by the solution of an over-determined system of linear equations. The paper describes the application of an iterative algorithm for the implementation of least square regression to solve this over-determined system directly in its rectangular form. The applied algorithm dynamically passes from an Ordinary Least Squares (OLS) problem to the regression problems known as Total Least Squares (TLS) and Data Least Squares (DLS). The obtained results suggest further investigations. In particular, the so called constrained least squares method is identified as an interesting development of the methodology.