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Dataplot Vol 1 Vol 2

BOX COX LINEARITY PLOT

Name:
    BOX-COX LINEARITY PLOT
Type:
    Graphics Command
Purpose:
    Generates a Box-Cox Linearity Plot.
Description:
    A Box-Cox linearity plot is a graphical technique for determining the Box-Cox transformation that yields the maximum correlation between two variables. Specifically, the correlation between (y,T(x)) where

      \( T_{x} = \frac{x^{\lambda}}{\lambda} \)

    is essentially the power-transformation family (adjusted to include log transformations).

    The horizontal axis is the lambda parameter. The vertical axis is the computed correlation coefficient between <y> and the transformed <x> The lambda corresponding to the highest correlation is the appropriate transformation to use in linearizing the relationship between <y> and <x>

Syntax 1:
    BOX-COX LINEARITY PLOT <y> <x>
                            <SUBSET/EXCEPT/FOR qualification>
    where <y> is the first response variable;
                <x> is the second response variable;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Syntax 2:
    REPLICATED BOX-COX LINEARITY PLOT <y> <x> <tag1>
                            <SUBSET/EXCEPT/FOR qualification>
    where <y> is the first response variable;
                <x> is the second response variable;
                <tag1> is a group-id variable;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.

    A Box-Cox linearity plot will be generated for each distinct value of the group-id variable. These plots will be overlaid on the same plot.

Syntax 3:
    REPLICATED BOX-COX LINEARITY PLOT <y> <x> <tag1> <tag2>
                            <SUBSET/EXCEPT/FOR qualification>
    where <y> is the first response variable;
                <x> is the second response variable;
                <tag1> is a group-id variable;
                <tag2> is a group-id variable; and where the <SUBSET/EXCEPT/FOR qualification> is optional.

    The two group-id variables are cross-tabulated and a Box-Cox linearity plot will be generated for each distinct combination of values for the group-id variables. These plots will be overlaid on the same plot.

Examples:
    BOX-COX LINEARITY PLOT Y X
    REPLICATED BOX-COX LINEARITY PLOT Y X TAG
Note:
    The number of observations in the two response variables (and any group-id variables) must be equal.
Note:
    The TO syntax is supported for the BOX COX LINEARITY command.
Default:
    None
Synonyms:
    BOX COX LINEARITY PLOT
Related Commands: References: Applications:
    Exploratory Data Analysis
Implementation Date:
    Pre-1987
    2010/5: Support for REPLICATION option
Program 1:
     
    SKIP 25
    READ BERGER1.DAT Y X
    LABEL CASE ASIS
    Y1LABEL Correlation
    X1LABEL Lambda
    BOX COX LINEARITY PLOT Y X
        
    plot generated by sample program
Program 2:
     
    title case asis
    title offset 2
    title automatic
    label case asis
    multiplot corner coordinates 0 0 100 95
    tic mark offset units screen
    y1tic mark offset 2 0
    .
    reset data
    skip 25
    read nelson.dat y x tag
    .
    replicated box cox linearity plot y x tag
        
    plot generated by sample program

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Date created: 11/30/2010
Last updated: 10/13/2015

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