A BASIC program for orthogonal polynomials and retrieval of regression coefficients for original model.

A fast, short method for calculating orthogonal polynomials has been programmed in BASIC. This is combined with the retrieval of b coefficients for the original, non-orthogonal model in, for example, a curvilinear regression. The program may be used alone, or in conjunction with a package of BASIC programs for weighted least-squares solutions, to which it forms an update. Transformation of the columns of an X, or design matrix, to orthogonal vectors can detect linear dependence among the columns, as well as supplying orthogonal polynomials for regression situations with unequal increments in x values, the values of the independent variable. Retrieval of the b coefficients for the original X matrix prior to transformation allows the user to insert any x value to obtain the corresponding predicted y (dependent variable) values.