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Multiple Regression using Matrices: Residual?

Hi.. I'm doing multiple regression on a dataset to estimate Y from X1
- Xn based on a covariance matrix calculated from the data Y, X1 ..

I can get a vector of deltas using the dot product of the subvector of
covariances between Y and X1 .. Xn,  and the covariance matrix of X1
.. Xn.

I then dot product this with a vector of my given X1 .. Xn to find my
estimated Y.  (Ye)

But I also need an indication of the confidence level, perhaps
indicated by the standard deviation of the residuals   (Y - Ye) for
each sample.

Trouble is, I don't want to calculate Ye  and compare with Y for every
single sample, I think there should be a way to get this using the
covariance matrix that I've already calculated.

How can I do this?  Is there another standard way to estimate the
confidence level?

I want to be able to say, "given this sample of X1 - Xn, I estimate Y
to be Ye plus or minus E to P% confidence level".. or I estimate Y to
be somewhere on a normal distribution with mean Ye and stdev S.

something like that.

Sorry if this sounds a little simplistic, I've never studied this
stuff at school.

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