Matrix Algebra Method For Deriving Oxide Factors And Its Relationship To The Principle Of Least Squares

Multiple regression analysis of glass property - composition data - involves the derivation of "normal equations", on for each oxide factor. The number of these is, in general, much smaller than the number of initial equations, which, for each composition, relate the property to the glass composition. Normal equations are readily derived by a matrix multiplication process. It is shown, by the use of a simple numerical example, that the method minimises the sum of squares of the residuals in the initial set of equations. The method is used to derive oxide factors for calculating thermal expansion coefficients of glasses in a number of systems.