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 .. Xn. 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.