Dear Sandra, R^2 is just a ratio between the amount of error explained between two models.
PRE (proportional reduction in error) = R^2 = (SSE model C - SSE model A)/SSE model C. This is sometimes expressed as (SSEc-SSEa)/SSEc = SSR/SSEc |SSR=sum squared reduced Given your example with some extensions: x<- c(1,2,3,4) y<- c(1.6,4.4,5.5,8.3) x.demean<-x-mean(x) y.mean<-mean(y) y.demean<-y-y.mean # The model is fit as before with all parameters. fit1<-lm(y~x) # includes intercept term summary(fit1) # PRE = 0.9749 fit1.SSE<-sum(resid(fit1)^2) # SSE=0.578 fit2<-lm(y~x-1) # excludes intercept, as in the original example (forces the intercept to zero) summary(fit2) # PRE = 0.9946 fit2.SSE<-sum(resid(fit2)^2) # SSE=0.6596667 # In order to understand the comparison taking place in fit1 SSEc <-sum(y.demean^2) #SSE of a model predicting only the mean SSEa <-fit1.SSE fit1.PRE <-(SSEc-fit1.SSE)/SSEc # = 0.9749 as by summary(lm(fit1)) SSEc.noint <-sum(y^2) # =121.06 fit2.PRE<-(SSEc.noint-fit2.SSE)/SSEc.noint # = 0.994551 or 0.9946 as before Hope this helps. Sincerely, KeithC. On 2010-06-11 2:16, Sandra Hawthorne wrote: > Hi, > > I'm trying to verify the calculation of coefficient of determination (r squared) for linear regression. I've done the calculation manually with a simple test case and using the definition of r squared outlined in summary(lm) help. There seems to be a discrepancy between the what R produced and the manual calculation. Does anyone know why this is so? What does the multiple r squared reported in summary(lm) represent? > > # The test case: > x<- c(1,2,3,4) > y<- c(1.6,4.4,5.5,8.3) > dummy<- data.frame(x, y) > fm1<- lm(y ~ x-1, data = dummy) > summary(fm1) > betax<- fm1$coeff[x] * sd(x) / sd(y) > # cd is coefficient of determination > cd<- betax * cor(y, x) ______________________________________________ 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.