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Dataplot Vol 2 Vol 1

DISTANCE FROM MEAN

Name:
    DISTANCE FROM MEAN (LET)
Type:
    Let Subcommand
Purpose:
    Compute the distance from the mean for a matrix.
Description:
    The quadratic form of a matrix M and a vector X is defined as:

      A=X'MX

    where X' is the transpose of X. If the vector X has n rows, then M must be an nxn matrix.

    The distance from the mean for a matrix X is a commonly used quadratic form:

      Di = (Xi - XBAR)'*SINV*(Xi-XBAR)

    where Xi is the ith row, XBAR is the vector of column means, and SINV is the inverse of the variance-covariance matrix of X. That is, Di is the distance of the ith row of the matrix from the mean. D is a vector.

    In Dataplot, you specify the original matrix, not the variance-covariance matrix.

Syntax:
    LET <y> = DISTANCE FROM MEAN <mat1>
    where <mat1> is a matrix for which the distance from the mean is to be computed;
    and where <y> is a vector where the resulting distances are saved.
Examples:
    LET Y = DISTANCE FROM MEAN M
Note:
    Matrices are created with either the READ MATRIX command or the MATRIX DEFINITION command. Enter HELP MATRIX DEFINITION and HELP READ MATRIX for details.
Default:
    None
Synonyms:
    None
Related Commands:
    READ MATRIX = Read a matrix.
    MATRIX COLUMN DIMENSION = Dimension maximum number of columns for Dataplot matrices.
    QUADRATIC FORM = Compute the quadratic form of a matrix and a vector.
    MATRIX DISTANCE = Compute various row and column distances for a matrix.
    MATRIX MEAN = Compute the overall mean for a matrix.
    MATRIX COLUMN STATISTIC = Compute column statistics for a matrix.
    MATRIX ROW STATISTIC = Compute row statistics for a matrix.
    LINEAR COMBINATION = Compute a linear combination of a matrix and a vector.
Reference:
    "Applied Multivariate Statistical Analysis", Third Edition, Johnson and Wichern, Prentice-Hall, 1992.
Applications:
    Multivariate Analysis
Implementation Date:
    1998/8
Program:
    SKIP 25
    READ MATRIX IRIS.DAT M
    LET Y = DISTANCE FROM MEAN M
    PRINT Y

Date created: 6/5/2001
Last updated: 4/4/2003
Please email comments on this WWW page to alan.heckert@nist.gov.