Tyson H, Fieldes M A
Comput Programs Biomed. 1982 Oct;15(2):151-4. doi: 10.1016/0010-468x(82)90067-8.
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.
一种用于计算正交多项式的快速、简短方法已用BASIC语言编程实现。此方法与例如在曲线回归中检索原始非正交模型的b系数相结合。该程序既可以单独使用，也可以与一组用于加权最小二乘解的BASIC程序结合使用，它是对这些程序的一种更新。将X矩阵（即设计矩阵）的列转换为正交向量，既可以检测列之间的线性相关性，也可以为自变量x值增量不等的回归情况提供正交多项式。在转换之前检索原始X矩阵的b系数，可让用户插入任何x值以获得相应的预测y（因变量）值。
