BOX COX LINEARITY PLOT

BOX-COX LINEARITY PLOT

Graphics Command

Generates a Box-Cox Linearity Plot.

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>

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.

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.

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.

BOX-COX LINEARITY PLOT Y X
REPLICATED BOX-COX LINEARITY PLOT Y X TAG

The number of observations in the two response variables (and any group-id variables) must be equal.

The TO syntax is supported for the BOX COX LINEARITY command.

None

BOX COX LINEARITY PLOT

BOX-COX NORMALITY PLOT	= Generates a Box-Cox normality plot.
BOX-COX HOMO PLOT	= Generates a Box-Cox homoscedasticity plot.
LINES	= Sets type for plot lines.
PROBABILITY PLOT	= Generates a probability plot.
PLOT	= Generates a data or function plot.

Box and Cox (1964), "An Analysis of of transformations," Journal of the Royal Statistical Society, Series B 26 (2): 211–252.

NIST/SEMATECH e-Handbook of Statistical Methods, Box-Cox Linearity Plot, 6/2003.

NIST/SEMATECH e-Handbook of Statistical Methods, Box-Cox Linearity Plot Used in a Case Study, 6/2003.

Exploratory Data Analysis

Pre-1987
2010/5: Support for REPLICATION option

 
SKIP 25
READ BERGER1.DAT Y X
LABEL CASE ASIS
Y1LABEL Correlation
X1LABEL Lambda
BOX COX LINEARITY PLOT Y X
    

 
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