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MULTIPLE_LINEAR_REGRESSION

MULTIPLE_LINEAR_REGRESSION

Name


    MULTIPLE_LINEAR_REGRESSION

Purpose


    This function will perform a full-order multiple linear regression
    by constructing a full-order design matrix including all possible
    combinations of the provided independent variables (for example, if
    5 independent variables are provided and a constant/intercept term is
    desired for a third-order model (order=3), then all 6-CHOOSE-3 three-
    term variable combinations will be placed in the design matrix).

Category


    Statistics.

Calling Sequence


    Result = $
      MULTIPLE_LINEAR_REGRESSION( independentData, $
                                  dependentData, $
                                  order, $
                                  [NO_INTERCEPT=no_intercept], $
                                  [DESIGN_MATRIX=design_matrix], $
                                  [ANALYSIS=analysis], $
                                  [SIGNIFICANCE_LEVEL=significance_level]

Inputs


    independentData
      A "number of independent variables" by "number of observations" array or
      a "number of observations" vector of independent variable values.
    dependentData
      A "number of observations" vector of dependent variable points.
    order
      The order of the model to be constructed. If a constant/intercept
      term is desired, the design matrix will be "number-of-variables"+1-
      CHOOSE-order by "number of observations" in size.

Keyword Parameters


    NO_INTERCEPT
      This keyword will cause a no-intercept regression to be carried out.
    DESIGN_MATRIX
      This keyword will cause the named variable to contain the constructed
      design matrix upon return.
    ANALYSIS
      This keyword will cause the named variable to contain a structure upon
      return that contains the regression analysis terms including:
          ANOVA
            A structure containing the elements of a multiple regression
            ANOVA table, including
                SSREGRESSION
                  The regression sum of squared error.
                SSRESIDUAL
                  The residual sum of squared error.
                SSTOTAL
                  The total sum of squared error.
                DOFREGRESSION
                  Regression degrees of freedom (p)
                DOFRESIDUAL
                  Residual degrees of freedom (n-p)
                DOFTOTAL
                  Total degrees of freedom (n-1)
                MSREGRESSION
                  The regression mean squared error.
                MSRESIDUAL
                  The residual mean squared error.
                MSTOTAL
                  The total mean squared error.
                F
                  The F-statistic used to determine the significance of
                  the regression (MSREGRESSION / MSRESIDUAL)
                PVALUE
                  The probability of exceeding the F-statistic for this
                  regression (if the p-Value is less than the significance
                  level, then the null hypothesis that all coefficients are
                  0 can be rejected and the regression is considered
                  significant)
                RSQUARED
                  The coefficient of determination.
          STANDARDERRORS
            A vector containing the standard error for each coefficient determined
            for the regression for using in significance testing.
          TVALUES
            A vector containing the t-value for each coefficient determined
            for the regression for using in significance testing.
          PVALUES
            A vector containing the p-value for each coefficient determined
            for the regression for using in significance testing.
          COEFFICIENTSSIGNIFICANT
            A vector containing values of 1 for each coefficient that was
            determined to be significant at a level of significance provided
            by the calling routine, and 0 otherwise.
    SIGNIFICANCE_LEVEL
      The named variable/constant contains the two-tailed level of significance
      at which the coefficients are evaluated (if not provided, a value of 0.05
      is used by default).

Return Value


    A "number of variables"+1-CHOOSE-order element vector containing the
    multiple linear regression coefficients for the constructed design matrix.
   

Side Effects


    None

Modification History


    Written by: Carl Salvaggio
                      Philip Salvaggio
    June, 2010 Original code
   

Disclaimer


    This source code is provided "as is" and without warranties as to performance
    or merchantability. The author and/or distributors of this source code may
    have made statements about this source code. Any such statements do not
    constitute warranties and shall not be relied on by the user in deciding
    whether to use this source code.
    This source code is provided without any express or implied warranties
    whatsoever. Because of the diversity of conditions and hardware under which
    this source code may be used, no warranty of fitness for a particular purpose
    is offered. The user is advised to test the source code thoroughly before
    relying on it. The user must assume the entire risk of using the source code.



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