[R] Partition of sums of squares (ANOVA)

[Bert Gunter]

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Bert

Bert Gunter
Genentech Nonclinical Biostatistics
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On Tue, Jul 22, 2014 at 10:53 AM, Marino David <davidmarino838 at gmail.com> wrote:
> Hi all r-mailling listers:
>
> Can anyone explain the theory (or the formula) about computing Sum Sq
> (color highligh below) related to regression items?  The link of Wikipedia (
> http://en.wikipedia.org/wiki/Partition_of_sums_of_squares) gives an
> introduction on how to calculate the total, model, and regression sum of
> squares. Is it similar to the Sum Sq computation? Is the regression sum of
> squares equal to (0.000437+ 0.002545+ 0.060984+ 0.062330+ 0.060480)?
>
> Any suggestion will be greatly appreciated.
>
> Thank you!
>
> David
>
> TraingData<-data.frame(
> x1=c(3.532,2.868,2.868,3.532,2.868,2.536,3.864),
> x2=c(1.992,1.992,1.328,1.328,1.328,1.66,1.66),
> y=c(9.040330254,8.900894412,8.701929163,9.057944749,8.701929163,8.74317832,9.10859913)
> )
> lm.sol<-lm(y~1+x1+x2+I(x1^2)+I(x2^2)+I(x1*x2),data=TraingData)
> anova(lm.sol)
>
> Analysis of Variance Table
>
> Response: y
>                 Df     *Sum Sq*     Mean       Sq F    value Pr(>F)
> x1              1    0.000437  0.000437    0.1055    0.8001
> x2              1    0.002545  0.002545    0.6141    0.5768
> I(x1^2)        1    0.060984  0.060984   14.7162    0.1623
> I(x2^2)        1    0.062330  0.062330   15.0409    0.1607
> I(x1 * x2)    1    0.060480  0.060480   14.5945    0.1630
> Residuals   1    0.004144  0.004144
>
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>
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