On 3/03/2008, at 1:58 PM, Louise Hoffman wrote:
> What if I need to calculate the variance for the fuel data?
>
> Are there a 'R' way to do that?
>
> I have derived
> variance = (Y-x*theta)^T * (Y - x*theta) / (n-p)
This should be (something like)
tr((Y - X%*%theta))%*%(Y-X%*%theta)/(n-p)
where X is your design matrix.
To get the information in R:
fit <- lm(fpi ~ rtime,data=fuelData)
summary(fit)
This tells you the residual standard error (standard deviation) is
7.681. Typing
summary(fit)$sigma
gives the answer to more decimal places --- 7.681288.
The residual variance can of course be obtained by
summary(fit)$sigma^2
Note that the name ``sigma'' is bad --- this terminology should
be reserved for population quantities. What we have is ``sigma-hat'',
an *estimate* of sigma.
Note also that for your fuel data the residual variance is pretty
much meaningless since your model is highly inappropriate for these
data.
cheers,
Rolf Turner
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