Mark Thank you! John John David Sorkin M.D., Ph.D. Chief, Biostatistics and Informatics University of Maryland School of Medicine Division of Gerontology Baltimore VA Medical Center 10 North Greene Street GRECC (BT/18/GR) Baltimore, MD 21201-1524 (Phone) 410-605-7119 (Fax) 410-605-7913 (Please call phone number above prior to faxing)
>>> Mark Leeds <marklee...@gmail.com> 2/18/2012 8:55 AM >>> Hi John: I don't understand what you're doing ( not saying that it's wrong. I just don't follow it ). Below is code for computing the coefficients using the matrix way I follow. Others may understand what you're doing and be able to fix it so I wouldn't just use below immediately. xprimex <- solve(t(data[,1:2]) %*% data[,1:2]) xprimey <- t(data[,1:2]) %*% data[,3] betas <- xprimex %*% xprimey print(betas) On Sat, Feb 18, 2012 at 8:36 AM, John Sorkin <jsor...@grecc.umaryland.edu>wrote: > I am trying to use matrix algebra to get the beta coefficients from a > simple bivariate linear regression, y=f(x). > The coefficients should be computable using the following matrix algebra: > t(X)Y / t(x)X > > I have pasted the code I wrote below. I clearly odes not work both because > it returns a matrix rather than a vector containing two elements the beta > for the intercept and the beta for x, and because the values produced by > the matrix algebra are not the same as those returned by the linear > regression. Can someone tell we where I have gone wrong, either in my use > of matrix algebra in R, or perhaps at a more fundamental theoretical level? > Thanks, > John > > # Define intercept, x and y. > int <- rep(1,100) > x <- 1:100 > y <- 2*x + rnorm(100) > > # Create a matrix to hold values. > data <- matrix(nrow=100,ncol=3) > dimnames(data) <- list(NULL,c("int","x","y")) > data[,"int"] <- int > data[,"x"] <- x > data[,"y"] <- y > data > > # Compute numerator. > num <- cov(data) > num > > # Compute denominator > denom <- solve(t(data) %*% data) > denom > > # Compute betas, [t(X)Y]/[t(X)Y] > betaRon <- num %*% denom > betaRon > > # Get betas from regression so we can check > # values obtaned by matrix algebra. > fit0 <- lm(y~x) > > > John David Sorkin M.D., Ph.D. > Chief, Biostatistics and Informatics > University of Maryland School of Medicine Division of Gerontology > Baltimore VA Medical Center > 10 North Greene Street > GRECC (BT/18/GR) > Baltimore, MD 21201-1524 > (Phone) 410-605-7119 > (Fax) 410-605-7913 (Please call phone number above prior to faxing) > > Confidentiality Statement: > This email message, including any attachments, is for ...{{dropped:17}} ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.