Class PolynomialRegression

  • public class PolynomialRegression
    extends MultipleLinearRegression
    A polynomial fit is a specific type of multiple regression. The simple regression model (a first-order polynomial) can be trivially extended to higher orders.

    The regression model y = b0 + b1*x + b2*x^2 + ... + bp*x^p + e is a system of polynomial equations of order p with polynomial coefficients { b0 ... bp}. The model can be expressed using data matrix x, target double[] y and parameter double[] ?. The ith row of X and Y will contain the x and y value for the ith data sample.

    The variables will be transformed in the following way: x => x1, ..., x^p => xp Then the model can be written as a multiple linear equation model: y = b0 + b1*x1 + b2*x2 + ... + bp*xp + e

    Elke Achtert
    • Field Detail

      • p

        public final int p
        The order of the polynom.
    • Constructor Detail

      • PolynomialRegression

        public PolynomialRegression​(double[] y,
                                    double[] x,
                                    int p)
        y - the (n x 1) - double[] holding the response values (y1, ..., yn)^T.
        x - the (n x 1)-double[] holding the x-values (x1, ..., xn)^T.
        p - the order of the polynom.
    • Method Detail

      • xMatrix

        private static double[][] xMatrix​(double[] x,
                                          int p)
      • adaptedCoefficientOfDetermination

        public double adaptedCoefficientOfDetermination()
        Returns the adapted coefficient of determination
        the adapted coefficient of determination
      • estimateY

        public double estimateY​(double x)
        Performs an estimation of y on the specified x value.
        x - the x-value for which y is estimated
        the estimation of y