While excluding the intercept may make sense, your formula for r^2 assumes that there was an intercept (that is why mean(y) is in your expression for sqtot).
Bill Dunlap Spotfire, TIBCO Software wdunlap tibco.com From: Pamela Krone-Davis [mailto:pkrone-da...@csumb.edu] Sent: Friday, July 13, 2012 10:32 AM To: William Dunlap Subject: Re: [R] R-squared with Intercept set to 0 (zero) for linear regression in R is incorrect Hi William, Thanks for getting back to me. When I use the values you provided, it would not make sense to set an intercept of 0. For my data, 0 does make sense as an intercept. When I do not set a 0 intercept using your data points, I get the same value for R-squared in R and in Excel and manually. Thanks Pam On Fri, Jul 13, 2012 at 10:03 AM, William Dunlap <wdun...@tibco.com<mailto:wdun...@tibco.com>> wrote: What does Excel give for the following data, where the by-hand formula you gave is obviously wrong? > x <- c(1, 2, 3) > y <- c(13.1, 11.9, 11.0) > M1 <- lm(y~x+0) > sqerr <- (y- predict(M1)) ^ 2 > sqtot <- (y - mean(y)) ^ 2 > 1 - sum(sqerr)/sum(sqtot) [1] -37.38707 Bill Dunlap Spotfire, TIBCO Software wdunlap tibco.com<http://tibco.com> > -----Original Message----- > From: r-help-boun...@r-project.org<mailto:r-help-boun...@r-project.org> > [mailto:r-help-boun...@r-project.org<mailto:r-help-boun...@r-project.org>] On > Behalf Of Pamela Krone-Davis > Sent: Friday, July 13, 2012 9:01 AM > To: r-help@r-project.org<mailto:r-help@r-project.org> > Subject: [R] R-squared with Intercept set to 0 (zero) for linear regression > in R is > incorrect > > Hi, > > I have been using lm in R to do a linear regression and find the slope > coefficients and value for R-squared. The R-squared value reported by R > (R^2 = 0.9558) is very different than the R-squared value when I use the > same equation in Exce (R^2 = 0.328). I manually computed R-squared and the > Excel value is correct. I show my code for the determination of R^2 in R. > When I do not set 0 as the intercept, the R^2 value is the same in R and > Excel. In both cases the slope coefficient from R and from Excel are > identical. > > k is a data frame with two columns. > > M1 = lm(k[,1]~k[,2] + 0) ## set intercept to 0 and get different > R^2 values in R and Excel > M2 = lm(k[,1]~k[,2]) > sumM1 = summary(M1) > sumM2 = summary(M2) ## get same value as Excel when intercept is not > set to 0 > > Below is what R returns for sumM1: > > lm(formula = k[, 1] ~ k[, 2] + 0) > > Residuals: > Min 1Q Median 3Q Max > -0.057199 -0.015857 0.003793 0.013737 0.056178 > > Coefficients: > Estimate Std. Error t value Pr(>|t|) > k[, 2] 1.05022 0.04266 24.62 <2e-16 *** > --- > Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 > > Residual standard error: 0.02411 on 28 degrees of freedom > Multiple R-squared: 0.9558, Adjusted R-squared: 0.9543 > F-statistic: 606.2 on 1 and 28 DF, p-value: < 2.2e-16 > > Way manual determination was performed. The value returned coincides with > the value from Excel: > > #### trying to figure out why the R^2 for R and Excel are so different. > sqerr = (k[,1] - predict(M1))^2 > sqtot = (k[,1] - mean(k[,1]) ^2 > > R2 = 1 - sum(sqerr)/sum(sqtot) ## for 1D get 0.328 same as > excel value > > I am very puzzled by this. How does R compute the value for R^2 in this > case? Did i write the lm incorrectly? > > Thanks > Pam > > PS In case you are interested, the data I am using for hte two columns is > below. > > k[, 1] > 1] > [1] 0.17170228 0.10881539 0.11843669 0.11619201 0.08441067 0.09424441 > 0.04782264 0.09526496 0.11596476 0.10323453 0.06487894 0.08916484 > 0.06358752 0.07945473 > [15] 0.11213532 0.06531185 0.11503484 0.13679548 0.13762677 0.13126827 > 0.12350649 0.12842441 0.13075654 0.15026602 0.14536351 0.07841638 > 0.08419016 0.11995240 > [29] 0.14425678 > > > k[,2] > [1] 0.11 0.10 0.11 0.10 0.10 0.09 0.10 0.09 0.09 0.11 0.09 0.10 0.09 0.10 > 0.09 0.10 0.10 0.10 0.11 0.10 0.11 0.11 0.12 0.13 0.15 0.10 0.09 0.11 0.12 > > > -- > Pam Krone-Davis > Project Research Assistant and Grant Manager > PO Box 22122 > Carmel, CA 93922 > (831)582-3684 (o) > (831)324-0391 (h) > > [[alternative HTML version deleted]] -- Pam Krone-Davis Project Research Assistant and Grant Manager PO Box 22122 Carmel, CA 93922 (831)582-3684 (o) (831)324-0391 (h) [[alternative HTML version deleted]] ______________________________________________ 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.
