Chapter 2: Regression

TCSCP

Transforms coefficients from a second order response surface model generated from squares and crossproducts of centered variables to a model using uncentered variables.

Required Arguments

XMEAN — Vector of length NVAR containing the means of the variables.   (Input)

SCPM — Vector of length NVAR(NVAR + 1)/2 containing the means of the generated square and crossproduct variables.   (Input)

Elements                              Description
1 to NVAR                              Squared variable means
NVAR+ 1 to NVAR * (NVAR + 1)/2            Crossproduct variable means

BC — Vector of length NVAR * (NVAR + 3)/2 + 1 containing the coefficients for the centered variables.   (Input)
Here, the fitted model is

            where zj = xj XMEAN(j) and mjk = j * NVAR j(j 1)/2 + k j. These regression coefficients can come from a regression using variables generated by routine GCSCP with the option ICEN = 1.

B — Vector of length NVAR * (NVAR + 3)/2 + 1 containing the coefficients of the uncentered variables.   (Output)
Here, the model uses the original x variables, i.e.,

Optional Arguments

NVAR — Number of variables.   (Input)
Default: NVAR = size (XMEAN,1).

FORTRAN 90 Interface

Generic:                              CALL TCSCP (XMEAN, SCPM, BC, B [,…])

Specific:                             The specific interface names are S_TCSCP and D_TCSCP.

FORTRAN 77 Interface

Single:                                CALL TCSCP (NVAR, XMEAN, SCPM, BC, B)

Double:                              The double precision name is DTCSCP.

Description

Routine TCSCP transforms coefficients from a second-order response surface model fitted using squares and crossproducts of centered variables into a model using the original uncentered variables. Let xij be the i-th setting of the j-th variable (i = 1, 2, , n; j = 1, 2, , m). Denote the means (stored in XMEAN) by

The settings of the j-th centered variable are given by

The settings of the j-th squared variable are given by

where

(stored in (m + j)-th column of SCPM) is the mean of the j-th squared variable. The settings of the jk crossproduct variable are given by

where

(stored in the

location of SCPM) is the mean of the jk-th (j < k) crossproduct variable. The fitted model is

TCSCP transforms the

to regression coefficients for the original independent variables. The fitted transformed model is

where

Comments

Crossproduct variables are ordered as follows: (1, 2), (1, 3), , (1, NVAR), (2, 3), (2, 4), , (2, NVAR), , (NVAR 1, NVAR).

Example

This example transforms coefficients from a second-order response surface model with three independent variables fitted using squares and crossproducts of centered variables into a model using the original uncentered variables.

 

      USE TCSCP_INT

      USE WRRRN_INT

 

      IMPLICIT   NONE

      INTEGER    NVAR

      PARAMETER  (NVAR=3)

!

      REAL       B(NVAR*(NVAR+3)/2+1), BC(NVAR*(NVAR+3)/2+1), &

                 SCPM(NVAR*(NVAR+1)/2), XMEAN(NVAR)

!

      DATA XMEAN/10.0, 11.0, 6.0/

      DATA SCPM/12.0, 5.0, 2.0, 3.0, 7.0, 1.0/

      DATA BC/1.0, 2.0, 3.0, 0.0, 5.0, 0.0, 7.0, 0.0, 9.0, 10.0/

!

      CALL TCSCP (XMEAN, SCPM, BC, B)

!

      CALL WRRRN ('B', B, 1, NVAR*(NVAR+3)/2+1, 1)

!

      END

Output

 

                                  B
     1        2        3        4        5        6        7        8
1753.0   -152.0    -57.0   -284.0      5.0      0.0      7.0      0.0

  9       10
9.0     10.0



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