RegressionResults (Apache Commons Math 3.3 API)

org.apache.commons.math3.stat.regression

## Class RegressionResults

- java.lang.Object
- - org.apache.commons.math3.stat.regression.RegressionResults

- All Implemented Interfaces:
    Serializable

      public class RegressionResults
      extends Object
      implements Serializable

  Results of a Multiple Linear Regression model fit.
  Since:
    3.0
  Version:
    $Id: RegressionResults.java 1392342 2012-10-01 14:08:52Z psteitz $
  See Also:
    Serialized Form

- - ### Constructor Summary

    Constructors
    Constructor and Description
    `RegressionResults(double[] parameters, double[][] varcov, boolean isSymmetricCompressed, long nobs, int rank, double sumy, double sumysq, double sse, boolean containsConstant, boolean copyData)` Constructor for Regression Results.

  - ### Method Summary

    Methods
    Modifier and Type | Method and Description
    --- | ---
    `double` | `getAdjustedRSquared()` Returns the adjusted R-squared statistic, defined by the formula
    `double` | `getCovarianceOfParameters(int i, int j)` Returns the covariance between regression parameters i and j.
    `double` | `getErrorSumSquares()` Returns the sum of squared errors (SSE) associated with the regression model.
    `double` | `getMeanSquareError()` Returns the sum of squared errors divided by the degrees of freedom, usually abbreviated MSE.
    `long` | `getN()` Returns the number of observations added to the regression model.
    `int` | `getNumberOfParameters()` Returns the number of parameters estimated in the model.
    `double` | `getParameterEstimate(int index)` Returns the parameter estimate for the regressor at the given index.
    `double[]` | `getParameterEstimates()` Returns a copy of the regression parameters estimates.
    `double` | `getRegressionSumSquares()` Returns the sum of squared deviations of the predicted y values about their mean (which equals the mean of y).
    `double` | `getRSquared()` Returns the coefficient of multiple determination, usually denoted r-square.
    `double` | `getStdErrorOfEstimate(int index)` Returns the standard error of the parameter estimate at index, usually denoted s(bindex).
    `double[]` | `getStdErrorOfEstimates()` Returns the standard error of the parameter estimates, usually denoted s(bi).
    `double` | `getTotalSumSquares()` Returns the sum of squared deviations of the y values about their mean.
    `boolean` | `hasIntercept()` Returns true if the regression model has been computed including an intercept.

    - ### Methods inherited from class java.lang.Object

      `clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`

- - ### Constructor Detail

    - #### RegressionResults

          public RegressionResults(double[] parameters,
                           double[][] varcov,
                           boolean isSymmetricCompressed,
                           long nobs,
                           int rank,
                           double sumy,
                           double sumysq,
                           double sse,
                           boolean containsConstant,
                           boolean copyData)

      Constructor for Regression Results.
      Parameters:
        `parameters` - a double array with the regression slope estimates
        `varcov` - the variance covariance matrix, stored either in a square matrix or as a compressed
        `isSymmetricCompressed` - a flag which denotes that the variance covariance matrix is in symmetric compressed format
        `nobs` - the number of observations of the regression estimation
        `rank` - the number of independent variables in the regression
        `sumy` - the sum of the independent variable
        `sumysq` - the sum of the squared independent variable
        `sse` - sum of squared errors
        `containsConstant` - true model has constant, false model does not have constant
        `copyData` - if true a deep copy of all input data is made, if false only references are copied and the RegressionResults become mutable

  - ### Method Detail

    - #### getParameterEstimate

          public double getParameterEstimate(int index)
                                      throws OutOfRangeException

      Returns the parameter estimate for the regressor at the given index.

      A redundant regressor will have its redundancy flag set, as well as a parameters estimated equal to `Double.NaN`

      Parameters:
        `index` - Index.
      Returns:
        the parameters estimated for regressor at index.
      Throws:
        `OutOfRangeException` - if `index` is not in the interval `[0, number of parameters)`.

    - #### getParameterEstimates

          public double[] getParameterEstimates()

      Returns a copy of the regression parameters estimates.

      The parameter estimates are returned in the natural order of the data.

      A redundant regressor will have its redundancy flag set, as will a parameter estimate equal to `Double.NaN`.

      Returns:
        array of parameter estimates, null if no estimation occurred

    - #### getStdErrorOfEstimate

          public double getStdErrorOfEstimate(int index)
                                       throws OutOfRangeException

      Returns the standard error of the parameter estimate at index, usually denoted s(bindex).
      Parameters:
        `index` - Index.
      Returns:
        the standard errors associated with parameters estimated at index.
      Throws:
        `OutOfRangeException` - if `index` is not in the interval `[0, number of parameters)`.

    - #### getStdErrorOfEstimates

          public double[] getStdErrorOfEstimates()

      Returns the standard error of the parameter estimates, usually denoted s(bi).

      If there are problems with an ill conditioned design matrix then the regressor which is redundant will be assigned `Double.NaN`.

      Returns:
        an array standard errors associated with parameters estimates, null if no estimation occurred

    - #### getCovarianceOfParameters

          public double getCovarianceOfParameters(int i,
                                         int j)
                                           throws OutOfRangeException

      Returns the covariance between regression parameters i and j.

      If there are problems with an ill conditioned design matrix then the covariance which involves redundant columns will be assigned `Double.NaN`.

      Parameters:
        `i` - `i`th regression parameter.
        `j` - `j`th regression parameter.
      Returns:
        the covariance of the parameter estimates.
      Throws:
        `OutOfRangeException` - if `i` or `j` is not in the interval `[0, number of parameters)`.

    - #### getNumberOfParameters

          public int getNumberOfParameters()

      Returns the number of parameters estimated in the model.

      This is the maximum number of regressors, some techniques may drop redundant parameters

      Returns:
        number of regressors, -1 if not estimated

    - #### getN

          public long getN()

      Returns the number of observations added to the regression model.
      Returns:
        Number of observations, -1 if an error condition prevents estimation

    - #### getTotalSumSquares

          public double getTotalSumSquares()

      Returns the sum of squared deviations of the y values about their mean.

      This is defined as SSTO here.

      If `n < 2`, this returns `Double.NaN`.

      Returns:
        sum of squared deviations of y values

    - #### getRegressionSumSquares

          public double getRegressionSumSquares()

      Returns the sum of squared deviations of the predicted y values about their mean (which equals the mean of y).

      This is usually abbreviated SSR or SSM. It is defined as SSM here

      Preconditions:

      - At least two observations (with at least two different x values) must have been added before invoking this method. If this method is invoked before a model can be estimated, `Double.NaN` is returned.
      Returns:
        sum of squared deviations of predicted y values

    - #### getErrorSumSquares

          public double getErrorSumSquares()

      Returns the sum of squared errors (SSE) associated with the regression model.

      The return value is constrained to be non-negative - i.e., if due to rounding errors the computational formula returns a negative result, 0 is returned.

      Preconditions:

      - numberOfParameters data pairs must have been added before invoking this method. If this method is invoked before a model can be estimated, `Double,NaN` is returned.
      Returns:
        sum of squared errors associated with the regression model

    - #### getMeanSquareError

          public double getMeanSquareError()

      Returns the sum of squared errors divided by the degrees of freedom, usually abbreviated MSE.

      If there are fewer than numberOfParameters + 1 data pairs in the model, or if there is no variation in `x`, this returns `Double.NaN`.

      Returns:
        sum of squared deviations of y values

    - #### getRSquared

          public double getRSquared()

      Returns the coefficient of multiple determination, usually denoted r-square.

      Preconditions:

      - At least numberOfParameters observations (with at least numberOfParameters different x values) must have been added before invoking this method. If this method is invoked before a model can be estimated, `Double,NaN` is returned.
      Returns:
        r-square, a double in the interval [0, 1]

    - #### getAdjustedRSquared

          public double getAdjustedRSquared()

      Returns the adjusted R-squared statistic, defined by the formula

           R2adj = 1 - [SSR (n - 1)] / [SSTO (n - p)]

      where SSR is the sum of squared residuals}, SSTO is the total sum of squares}, n is the number of observations and p is the number of parameters estimated (including the intercept).

      If the regression is estimated without an intercept term, what is returned is

            1 - (1 - getRSquared() ) * (n / (n - p))

      Returns:
        adjusted R-Squared statistic

    - #### hasIntercept

          public boolean hasIntercept()

      Returns true if the regression model has been computed including an intercept. In this case, the coefficient of the intercept is the first element of the `parameter estimates`.
      Returns:
        true if the model has an intercept term

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