Dataplot Vol 2 Vol 1

# CATCHER MATRIX

Name:
CATCHER MATRIX (LET)
Type:
Let Subcommand
Purpose:
Compute the catcher matrix.
Description:
The catcher matrix is defined as:

C = X(X'X)-1

The X matrix is typically a design matrix for a multiple linear regression.

The catcher matrix is useful for many regression diagnostic computations. For example, the help for the FIT command describes the use of the catcher matrix in generating partial regression plots, partial leverage plots, and variance inflation factors.

This command simplifies writing macros to compute these, as well as other, regression diagnostics. Although this matrix can also be computed using Dataplot matrix commands, this requires the creation of a large number of data columns.

Syntax:
LET <mat2> = CATCHER MATRIX <mat1>             <SUBSET/EXCEPT/FOR qualification>
where <mat1> is the design matrix for which the catcher matrix is to be computed;
<mat2> is a matrix where the resulting catcher matrix is saved;
and where the <SUBSET/EXCEPT/FOR qualification> is optional (and rarely used in this context).
Examples:
LET C = CATCHER MATRIX X
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.
Note:
The columns of a matrix are accessible as variables by appending an index to the matrix name. For example, the 4x4 matrix C has columns C1, C2, C3, and C4. These columns can be operated on like any other DATAPLOT variable.
Note:
The maximum size matrix that DATAPLOT can handle is set when DATAPLOT is built on a particular site. Enter the command HELP MATRIX DIMENSION for details on the maximum size matrix that can be accomodated.
Default:
None
Synonyms:
None
Related Commands:
 FIT = Perform a least squares fit. MATRIX DIEMNSION = Specify the dimensions for matrices. MATRIX EIGENVALUES = Compute the matrix eigenvalues. MATRIX EIGENVECTORS = Compute the matrix eigenvectors. MATRIX EUCLID NORM = Compute the matrix Euclidean norm. MATRIX MULTIPLICATION = Perform a matrix multiplication. MATRIX SOLUTION = Solve a system of linear equations. MATRIX INVERSE = Compute a the inverse of a matrix. CORRELATION MATRIX = Compute the correlation matrix of a matrix. VARIANCE-COVARIANCE MATRIX = Compute the variance-covariance matrix of a matrix. PRINCIPLE COMPONENTS = Compute the principle components of a matrix. SINGULAR VALUE DECOMPOSITION = Compute the singular value decomposition of a matrix.
Reference:
"Applied Linear Statistical Models", 3rd ed., Neter, Wasserman, and Kunter, 1990, Irwin.

"Applied Regression Analysis", 2nd ed., Draper and Smith, John Wiley, 1981.

"Residuals and Influence in Regression", Cook and Weisberg, Chapman and Hall, 1982.

"Regression Diagnostics", Belsley, Kuh, and Welsch, John Wiley, 1980.

Applications:
Regression Diagnostics
Implementation Date:
2002/6
Program:
```DIMENSION 100 COLUMNS
SKIP 25
READ HALD647.DAT Y X1 X2 X3 X4
SKIP 0
LET N = SIZE X1
LET X0 = SEQUENCE 1 1 N
WRITE TEMP.DAT X0 X1 X2 X3 X4
DELETE X0 X1 X2 X3 X4
LET C = CATCHER MATRIX X
PRINT C
```
This generates the following output:
```         MATRIX C       --           13 ROWS
--            5 COLUMNS

VARIABLES--C1             C2             C3             C4             C5

0.4011422E-02 -0.2106577E-01  0.3952163E-02 -0.2795892E-01  0.1151358E-01
-0.1588606E-01 -0.1082202E-01  0.2104739E-02  0.9455606E-03  0.5202264E-02
-0.6491054E-01  0.3285703E-01  0.3380285E-02  0.2794100E-01 -0.6873165E-02
-0.9498145E-02  0.1991004E-01 -0.3383397E-02  0.7536128E-02  0.2286427E-02
0.1443816E-01 -0.3764334E-01  0.9528174E-02 -0.3966242E-01  0.8826852E-02
-0.2858971E-01  0.2079069E-01  0.1318561E-02  0.1466443E-01 -0.3797196E-02
-0.4519707E-01  0.3504255E-02  0.6955454E-02  0.2207738E-01 -0.7556211E-02
0.9131871E-02  0.9094987E-02 -0.6867160E-02  0.2402785E-01 -0.2229009E-03
0.6397810E-02 -0.1138435E-01  0.1831780E-02  0.4145637E-02 -0.6963555E-03
0.6396443E-02  0.5269508E-01 -0.9566874E-02  0.2026298E-01 -0.4618318E-02
0.2705855E-01  0.1574513E-02 -0.6509373E-02  0.1813316E-01 -0.8013789E-03
0.3462283E-01 -0.1258131E-01  0.2497504E-02 -0.1914054E-01  0.1119057E-02
0.5911485E-01 -0.3539623E-01  0.5134115E-02 -0.4108119E-01  0.5439803E-02
```

Date created: 6/6/2002
Last updated: 4/4/2003