Multilinear regression: Using SOL regression to explore the expectation space and using experimental designs to determine the best solution

摘要

Classical multilinear regression [1-3] provides just one solution which is obtained by the least-squares method. PLS (Partial least squares) regression [4-6] has as many solutions as the number of coefficients in the mathematical model. Among these solutions it is then possible to choose the one which meets, at the best, a criterion of optimization. But the number of solutions is limited and the best solution could be between two PLS' solutions and the optimization is only partial. This is why Sequential Orthogonal Linear (or SOL) regression was proposed. This regression has an infinite number of solutions and the expectation space is entirely covered. It is then possible to find the best solution using experimental designs or statistical optimization tools as simplex, golden section or Fibonacci series.