A Pascal program for weighted least squares regression on a microcomputer.

Abstract

Weighted least-squares regression has been programmed in Pascal for a microcomputer. A double precision Pascal compiler and the Motorola 6809 assembler produce a fast machine-code program occupying 22,000 bytes of memory when appended to the Pascal run-time module. Large data sets fit in the remaining memory. A regression with 72 observations and 24 parameters runs in 7 min, excluding optional print out of large matrices. The maximum dimensions of the design matrix, X, can be altered by modifying two Pascal constants. Minor changes to the Pascal source program will make it compatible with other Pascal compilers. The program optionally orthogonalises the X matrix to detect linearly-dependent columns in X, and/or generate orthogonal parameter estimates. After orthogonalizing X and fitting the model, the parameter estimates for the original X can be retrieved by the program. Regressions on a repeatedly reduced model are performed through elimination of columns in X until the minimum adequate model is obtained.