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# rscanon()

Usage:
 ```rscanon(y,x1,x2,...,xk [,block:var1,block:var2,...]), REAL vectors y, x1, ...,xk, factors var1, var2, ...; all should have the same number of rows. ```

Keywords: analysis
```rscanon(y,x1,x2,...,xk) performs the canonical analysis for the
quadratic response surface model with response y and predictors x1,
... , xk.  y and x1 through xk must be REAL vectors of the same length.

The result is a structure with components 'b0', 'b', 'B', 'x0', 'y0',
'H', and 'lambda', giving the intercept, linear coefficients, the
quadratic/ cross product coefficient matrix, the stationary point, the
predicted response at the stationary point, the matrix of canonical
directions, and the eigenvalues, respectively.

If the design was blocked, you can specify the blocking factors using
one or more keyword phrases of the form 'block:var', where var is a
factor.  For example, if the design was blocked by factors date and
analyst, you might use
Cmd> rscanon(yield,time,temperature,block:date,block:analyst).
The output is the same as before, but is block adjusted.

Examples:
Cmd> #data from example 16-2 of Montgomery

Cmd> x1 <- vector(-1,-1,1,1,0,0,0,0,0,1.414,-1.414,0,0)

Cmd> x2 <- vector(-1,1,-1,1,0,0,0,0,0,0,0,1.414,-1.414)

Cmd> y <- vector(76.5,77.0,78.0,79.5,79.9,80.3,80.0,79.7,\
79.8,78.4,75.6,78.5,77.0)

Cmd> rscanon(y,x1,x2)
component: b0
(1)        79.94
component: b
(1)      0.99505       0.5152
component: B
(1,1)      -1.3764        0.125
(2,1)        0.125      -1.0013
component: x0
(1)      0.38923      0.30585
component: y0
(1)       80.212
component: H
(1,1)      0.28972      0.95711
(2,1)      0.95711     -0.28972
component: lambda
(1)      -0.9635      -1.4143
```

Gary Oehlert 2003-01-15