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

H Tyson, M A Fieldes

    Computer Programs in Biomedicine
    |October 1, 1982
    PubMed
    Summary
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    This study presents a fast BASIC program for calculating orthogonal polynomials and retrieving regression coefficients. This method aids in analyzing curvilinear regression models and predicting dependent variable values.

    Area of Science:

    • Statistics
    • Computational Mathematics

    Background:

    • Orthogonal polynomials are crucial for regression analysis, especially with non-uniform data.
    • Existing methods for calculating orthogonal polynomials can be computationally intensive.

    Purpose of the Study:

    • To develop a fast and efficient BASIC program for calculating orthogonal polynomials.
    • To integrate this calculation with the retrieval of regression coefficients for non-orthogonal models.

    Main Methods:

    • A novel, short algorithm for calculating orthogonal polynomials programmed in BASIC.
    • Integration with existing BASIC programs for weighted least-squares solutions.
    • Transformation of design matrix columns to orthogonal vectors.

    Main Results:

    Related Experiment Videos

    • The program efficiently calculates orthogonal polynomials and retrieves original regression coefficients.
    • Column transformation detects linear dependence in the design matrix.
    • Enables regression analysis with unequal increments in independent variable values.

    Conclusions:

    • The developed BASIC program offers a fast and updated method for orthogonal polynomial calculation.
    • It enhances regression analysis by detecting multicollinearity and handling unevenly spaced data.
    • Facilitates accurate prediction of dependent variables using original model coefficients.