Methods and systems for fast least squares optimization for analysis of variance with covariants

A method of linear regression for modeling effects of multiple variables on uni-variable or multi-variable outputs, said method comprising the steps of:

• subdividing a matrix containing rows and columns of data representing the multiple variables into q mutually exhaustive bins of columns, each said column representing one of the multiple variables;
• applying a modified Gauss-Seidel algorithm iteratively to said bins for all 1 to q bins for a complete pass through the matrix;
• and
• repeating said iteratively applying the modified Gauss-Seidel algorithm over a number of complete passes until changes in calculated values of a solution matrix B resultant from linearly regressing the output variables on the matrix containing the multiple variables over a complete pass of all bins become smaller in magnitude than a predetermined threshold magnitude, or until a preset maximum number of complete passes have been performed, as necessary to end a cycle convergence.

A system for performing fast linear regression for modeling effects of multiple variables on uni-variable or multi-variable outputs, said system comprising:

• a feature for modeling the multiple variables as a matrix wherein each row of the matrix represents one of the variables or a level of one of the variables of the multiple variables;
• a feature for subdividing the matrix q mutually exhaustive bins of columns, each said bin comprising at least one column;
• a feature for applying a modified Gauss-Seidel algorithm iteratively to said bins for all 1 to q bins for a complete pass through the matrix for linear regression of the output variables on the multiple variables per bin;
• and
• a feature for repeating said iterative application of the modified Gauss-Seidel algorithm over a number of complete passes until changes in calculated values of a solution matrix B resultant from linearly regressing the output variables on the matrix containing the multiple variables when comparing a current complete pass to a next previous complete pass become smaller in magnitude than a predetermined threshold magnitude, or until a preset maximum number of complete passes have been performed, as necessary to end a cycle convergence.

A computer readable medium carrying one or more sequences of instructions for analysis of variance, wherein execution of one or more sequences of instructions by one or more processors causes the one or more processors to perform the steps of:

• modeling variables, including nominal and/or ordinal as well as scalar variables, relative to one or more measured outputs according to the equation:
• XB=Y
• where
• X is a matrix containing rows and columns of data representing the variables;
• Y is a vector or matrix with a column for every actual dependent variable of the measured outputs;
• and
• B is the solution matrix or vector containing a column for each response column in Y, that defines the effects of the variables in X;
• partitioning columns of X into q mutually exhaustive bins of said columns;
• iteratively solving for values of the solution matrix of the model for each bin 1 to q for a pass through the entire X matrix;
• and
• repeating said iteratively solving for a number of passes until changes in calculated values of the solution matrix B become smaller in magnitude than a predetermined threshold magnitude, or until a preset maximum number of passes have been performed, as necessary to end a cycle convergence.