Package elki.math.statistics

Class MultipleLinearRegression

  • Direct Known Subclasses:
    PolynomialRegression
    public class MultipleLinearRegression
extends java.lang.Object
    Multiple linear regression attempts to model the relationship between two or more explanatory variables and a response variable by fitting a linear equation to observed data. Every value of the independent variable x is associated with a value of the dependent variable y.

    The population regression line for p explanatory variables x1, x2, ... , xp is defined to be y = b0 + b1*x1 + b2*x2 + ... + bp*xp + e.

    Since:
    0.1
    Author:
    Elke Achtert

    • Field Summary

      Fields 
      Modifier and Type Field Description
      private double[] b
      The (p+1 x 1) - double[] holding the estimated b-values (b0, b1, ..., bp)^T.
      private double[] e
      The (n x 1) - double[] holding the estimated residuals (e1, ..., en)^T.
      private double ssr
      The sum of square residuals
      private double sst
      The sum of square totals
      private double variance
      The error variance.
      private double[][] x
      The (n x p+1)-matrix holding the x-values, where the i-th row has the form (1 x1i ... x1p).
      private double[][] xx_inverse
      Holds the matrix (x'x)^-1.
      private double[] y
      The (n x 1) - double[] holding the y-values (y1, ..., yn)^T.
      private double y_mean
      Holds the mean value of the y-values.

    • Constructor Summary

      Constructors 
      Constructor Description
      MultipleLinearRegression​(double[] y, double[][] x)
      Constructor.

    • Field Detail

      • y

        private final double[] y
        The (n x 1) - double[] holding the y-values (y1, ..., yn)^T.

      • y_mean

        private final double y_mean
        Holds the mean value of the y-values.

      • x

        private final double[][] x
        The (n x p+1)-matrix holding the x-values, where the i-th row has the form (1 x1i ... x1p).

      • b

        private final double[] b
        The (p+1 x 1) - double[] holding the estimated b-values (b0, b1, ..., bp)^T.

      • e

        private final double[] e
        The (n x 1) - double[] holding the estimated residuals (e1, ..., en)^T.

      • variance

        private final double variance
        The error variance.

      • xx_inverse

        private final double[][] xx_inverse
        Holds the matrix (x'x)^-1.

      • ssr

        private final double ssr
        The sum of square residuals

      • sst

        private final double sst
        The sum of square totals

    • Constructor Detail

      • MultipleLinearRegression

        public MultipleLinearRegression​(double[] y,
                                double[][] x)
        Constructor.
        Parameters:
        y - the (n x 1) - double[] holding the response values (y1, ..., yn)^T.
        x - the (n x p+1)-matrix holding the explanatory values, where the i-th row has the form (1 x1i ... x1p).

    • Method Detail

      • toString

        public java.lang.String toString()
        Returns a string representation of the object.
        Overrides:
        toString in class java.lang.Object
        Returns:
        a string representation of the object.

      • getSumOfSquaresTotal

        public double getSumOfSquaresTotal()
        Returns the sum of squares total.
        Returns:
        the sum of squares total

      • getSumOfSquareResiduals

        public double getSumOfSquareResiduals()
        Returns the sum of square residuals.
        Returns:
        the sum of square residuals

      • getEstimatedCoefficients

        public double[] getEstimatedCoefficients()
        Returns the estimated coefficients
        Returns:
        the estimated coefficients

      • getEstimatedResiduals

        public double[] getEstimatedResiduals()
        Returns the estimated residuals
        Returns:
        the estimated residuals

      • coefficientOfDetermination

        public double coefficientOfDetermination()
        Returns the coefficient of determination
        Returns:
        the coefficient of determination

      • estimateY

        public double estimateY​(double[][] x)
        Perform an estimation of y on the specified matrix.
        Parameters:
        x - the matrix for which y is estimated
        Returns:
        the estimation of y

      • getVariance

        public double getVariance()
        Returns the error variance.
        Returns:
        the error variance