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## org.statcato.statistics.inferential
Class MultipleRegression

    java.lang.Object
      org.statcato.statistics.inferential.MultipleRegression

    public class MultipleRegression

extends java.lang.Object

Multiple regression.

Since:
  1.0
Version:
  %I%, %G%
Author:
  Margaret Yau

Constructor Summary
`MultipleRegression(java.util.Vector<java.util.Vector<java.lang.Double>> IndependentVars, java.util.Vector<java.lang.Double> DependentVar, boolean hasConstant)` Constructor.

Method Summary
`double` | `AdjustedCoefficientOfDetermination()` Returns the adjusted coefficient of determination.
`double` | `CoefficientOfDetermination()` Returns the coefficient of determination r^2, the amount of the variation in y that is explained by the regression line.
`double` | `ExplainedVariation()` Returns the explained variation (the sum of squared differences between the predicted y value and the average y value).
`int` | `NumIndepVar()` Returns the number of independent variables.
`double` | `PValue()` Returns the p-Value of test statistics.
`Jama.Matrix` | `RegressionEqCoefficients()` Returns the coefficients of the regression equation y = b_0 + b_1 * x_1 + ...
`int` | `SampleSize()` Returns the sample size.
`double` | `StandardError()` Returns the standard error of estimate, sqrt(unexplained variation / (n-2)).
`double` | `TestStatistics()` Returns the test statistics F.
`java.lang.String` | `toString()`
`double` | `TotalVariation()` Returns the total variation (the sum of squared differences between the y values and the average y value).
`double` | `UnexplainedVariation()` Returns the unexplained variation (the sum of squared differences between the predicted y value and the y value).
`Jama.Matrix` | `XVar(int i)` Returns the i th value of all the independent variables as a 1 by k matrix.
`double` | `YPredicted(Jama.Matrix var)` Returns the predicted y value given a vector of values of the independent variables using the regression equation.

Methods inherited from class java.lang.Object
`clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait`

Constructor Detail

### MultipleRegression

    public MultipleRegression(java.util.Vector<java.util.Vector<java.lang.Double>> IndependentVars,
                              java.util.Vector<java.lang.Double> DependentVar,
                              boolean hasConstant)

  Constructor.

  Parameters:
    `IndependentVars` - a vector of vectors of double, where each vector is an independent variable with the same number of values
    `DependentVar` - a vector of double, which has the same number of values as the independent variables

Method Detail

### RegressionEqCoefficients

    public Jama.Matrix RegressionEqCoefficients()

  Returns the coefficients of the regression equation y = b_0 + b_1 * x_1 + ... + b_k * x_k as a matrix of dimension k+1 by 1: [b_0 b_1 ... b_k]'.

  Returns:
    a k+1 by 1 matrix containing the coefficients of the regression equation

### YPredicted

    public double YPredicted(Jama.Matrix var)

  Returns the predicted y value given a vector of values of the independent variables using the regression equation.

  Parameters:
    `var` - a vector of double that has the same number of values as the number of independent variables.
  Returns:
    predicted y value

### TotalVariation

    public double TotalVariation()

  Returns the total variation (the sum of squared differences between the y values and the average y value).

  Returns:
    total variation

### XVar

    public Jama.Matrix XVar(int i)

  Returns the i th value of all the independent variables as a 1 by k matrix.

  Parameters:
    `i` - index
  Returns:
    matrix

### ExplainedVariation

    public double ExplainedVariation()

  Returns the explained variation (the sum of squared differences between the predicted y value and the average y value).

  Returns:
    explained variation

### UnexplainedVariation

    public double UnexplainedVariation()

  Returns the unexplained variation (the sum of squared differences between the predicted y value and the y value).

  Returns:
    unexplained variation

### CoefficientOfDetermination

    public double CoefficientOfDetermination()

  Returns the coefficient of determination r^2, the amount of the variation in y that is explained by the regression line.

  Returns:
    r^2

### AdjustedCoefficientOfDetermination

    public double AdjustedCoefficientOfDetermination()

  Returns the adjusted coefficient of determination.

  Returns:
    r^2

### StandardError

    public double StandardError()

  Returns the standard error of estimate, sqrt(unexplained variation / (n-2)).

  Returns:
    s

### TestStatistics

    public double TestStatistics()

  Returns the test statistics F. F = (explained variation) / (unexplained variation) * (n - k - 1) / k

  Returns:
    test statistics F

### PValue

    public double PValue()

  Returns the p-Value of test statistics.

  Returns:
    p-Value

### SampleSize

    public int SampleSize()

  Returns the sample size.

  Returns:
    n

### NumIndepVar

    public int NumIndepVar()

  Returns the number of independent variables.

  Returns:
    k

### toString

    public java.lang.String toString()

  Overrides:
    `toString` in class `java.lang.Object`

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