# [R] 4^2 factorial help

Liaw, Andy andy_liaw at merck.com
Fri Aug 18 14:45:11 CEST 2006

```If you really want the quadratic terms, you need to keep those variables as
numeric, instead of factors.  (You might also want to look into something
like the central composite designs.)

summary() and coef() on the resulting fitted object should give you want you
need.  Things like these are covered in the "An Introduction to R" manual...

Andy

From: lcorreia at sun.ac.za
>
> To whom it may concern:
>
> I am trying a factorial design a system of mine that has two factors.
> Each factor was set at four different levels, with one
> replication for each of the combinations. My data is as follows:
>
>
>            A           B                     Response
>
> 1        600        2.5                   0.0257
>
> 2        600        2.5                   0.0254
>
> 3        600        5                      0.0217
>
> 4        600        5                      0.0204
>
> 5        600        10                    0.0191
>
> 6        600        10                    0.0210
>
> 7        600        20                    0.0133
>
> 8        600        20                    0.0139
>
> 9        800        2.5                   0.0312
>
> 10       800       2.5                   0.0317
>
> 11       800       5                      0.0307
>
> 12       800      5                      0.0309
>
> 13       800       10                    0.0330
>
> 14       800       10                    0.0318
>
> 15       800       20                    0.0225
>
> 16       800       20                    0.0234
>
> 17      1000      2.5                   0.0350
>
> 18      1000      2.5                   0.0352
>
> 19      1000      5                      0.0373
>
> 20      1000      5                      0.0361
>
> 21      1000     10                    0.0432
>
> 22      1000     10                    0.0402
>
> 23      1000     20                    0.0297
>
> 24      1000     20                    0.0306
>
> 25      1200      2.5                   0.0324
>
> 26      1200      2.5                   0.0326
>
> 27      1200      5                      0.0353
>
> 28      1200      5                      0.0353
>
> 29      1200     10                    0.0453
>
> 30      1200     10                    0.0436
>
> 31      1200     20                    0.0348
>
> 32      1200     20                    0.0357
>
>
>
> I am able to enter my data into R and obtain an ANOVA table
> (which I have been able to verify as correct using an excel
> spreadsheet), using the following syntax:
>
>
>
> >Factorial<-data.frame(A=c(rep(c("600", "600", "600", "600", "800",
> "800", "800", "800", "1000", "1000", "1000", "1000", "1200",
> "1200", "1200", "1200"), each=2)), B=c(rep(c("2.5", "5",
> "10", "20", "2.5", "5", "10", "20", "2.5", "5", "10", "20",
> "2.5", "5", "10", "20"), each=2)), Response = c(0.0257,
> 0.0254, 0.0217, 0.0204, 0.0191, 0.021, 0.0133, 0.0139,
> 0.0312, 0.0317, 0.0307, 0.0309, 0.033, 0.0318, 0.0225,
> 0.0234, 0.035, 0.0352, 0.0373, 0.0361, 0.0432, 0.0402,
> 0.0297, 0.0306, 0.0324, 0.0326, 0.0353, 0.0353, 0.0453,
> 0.0436, 0.0348, 0.0357))
>
>
>
> > anova(aov(Response~A*B, data=Factorial))
>
>
>
> However, this is as far as I am able to go. I would like to
> obtain the coefficients of my model, but am unable. I would
> also like to use other non-linear models as these factors are
> not linear. Also would like to add A^2 and B^2 into the ANOVA
> and modeling.
>
>
>
> help is much appreciated.
>
>
>
> Yours sincerely,
>
> Leslie Correia
>
> ------------------------------------------------
>
> Department of Process Engineering
>
> University of Stellenbosch
>
> Private Bag X1
>
> Matieland, 7602
>
> Stellenbosch
>
> Tel:   0837012017
>
> E-mail: lcorreia at sun.ac.za <mailto:lcorreia at sun.ac.za>
>
> ------------------------------------------------
>
>
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