[R] R-squared with Intercept set to 0 (zero) for linear regression in R is incorrect

[William Dunlap]

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


> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On
> Behalf Of Pamela Krone-Davis
> Sent: Friday, July 13, 2012 9:01 AM
> To: r-help at 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)
> 
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