Try multiplying var(e) by n-1 and dividing by n-3 (97 are the degrees of freedom for the sum of squares error in your example). Then it all matches up nicely.
Best, -- Wolfgang Viechtbauer Department of Methodology and Statistics University of Maastricht, The Netherlands http://www.wvbauer.com/ ----Original Message---- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Daniel Malter Sent: Tuesday, February 26, 2008 08:25 To: 'r-help' Subject: [R] OLS standard errors > Hi, > > the standard errors of the coefficients in two regressions that I > computed by hand and using lm() differ by about 1%. Can somebody help > me to identify the source of this difference? The coefficient > estimates are the same, but the standard errors differ. > > ####Simulate data > > happiness=0 > income=0 > gender=(rep(c(0,1,1,0),25)) > for(i in 1:100){ > happiness[i]=1000+i+rnorm(1,0,40) > income[i]=2*i+rnorm(1,0,40) > } > > ####Run lm() > > reg=lm(happiness~income+factor(gender)) > summary(reg) > > ####Compute coefficient estimates "by hand" > > x=cbind(income,gender) > y=happiness > > z=as.matrix(cbind(rep(1,100),x)) > beta=solve(t(z)%*%z)%*%t(z)%*%y > > ####Compare estimates > > cbind(reg$coef,beta) ##fine so far, they both look the same > > reg$coef[1]-beta[1] > reg$coef[2]-beta[2] > reg$coef[3]-beta[3] ##differences are too small to cause a 1% > difference > > ####Check predicted values > > estimates=c(beta[2],beta[3]) > > predicted=estimates%*%t(x) > predicted=as.vector(t(as.double(predicted+beta[1]))) > > cbind(reg$fitted,predicted) ##inspect fitted values > as.vector(reg$fitted-predicted) ##differences are marginal > > #### Compute errors > > e=NA > e2=NA > for(i in 1:length(happiness)){ > e[i]=y[i]-predicted[i] ##for "hand-computed" regression > e2[i]=y[i]-reg$fitted[i] ##for lm() regression > } > > #### Compute standard error of the coefficients > > sqrt(abs(var(e)*solve(t(z)%*%z))) ##for "hand-computed" regression > sqrt(abs(var(e2)*solve(t(z)%*%z))) ##for lm() regression using e2 > from > above > > ##Both are the same > > ####Compare to lm() standard errors of the coefficients again > > summary(reg) > > > The diagonal elements of the variance/covariance matrices should be > the standard errors of the coefficients. Both are identical when > computed by hand. However, they differ from the standard errors > reported in summary(reg). The difference of 1% seems nonmarginal. > Should I have multiplied var(e)*solve(t(z)%*%z) by n and divided by > n-1? But even if I do this, I still observe a difference. Can anybody > help me out what the source of this difference is? > > Cheers, > Daniel > > > ------------------------- > cuncta stricte discussurus > > ______________________________________________ > 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. ______________________________________________ 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.
