Multiple Regression using Matrices: Residual?
- To: mathgroup at smc.vnet.net
- Subject: [mg52437] Multiple Regression using Matrices: Residual?
- From: lindseyp at gmail.com (lindseyp)
- Date: Sat, 27 Nov 2004 01:40:34 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
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
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
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
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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