# [R] Question about linear regression in R

John Fox jfox at mcmaster.ca
Tue Nov 15 14:46:23 CET 2011

```Dear Miles,

Within rounding error, you got the right intercept, log(3); slope, 0;
residuals, all 0; residual standard error, 0; and standard errors of the
intercept and slope, both 0. The R^2 should have been undefined (i.e., 0/0),
but dividing one number that's 0 within rounding error by another gives a
wild result. Likewise for the omnibus F and t-test for the slope. The moral:
don't expect floating-point arithmetic on a computer to be perfectly
precise.

I hope this helps,
John

--------------------------------
John Fox
Senator William McMaster
Professor of Social Statistics
Department of Sociology
McMaster University
Hamilton, Ontario, Canada
http://socserv.mcmaster.ca/jfox

> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-
> project.org] On Behalf Of Miles Yang
> Sent: November-14-11 10:49 PM
> To: r-help-request at r-project.org; r-help at r-project.org
> Subject: [R] Question about linear regression in R
>
> Hi all,
> I wrote a r program as below:
>
> x <- 1:10
> y <- c(3,3,3,3,3,3,3,3,3,3)
>
> fit <- lm(log(y) ~ x)
> summary(fit)
>
> And I expect to get some error message from R, because "y" is constant.
> But, I got the message as below:
>
> > summary(fit)
>
> Call:
> lm(formula = log(y) ~ x)
>
> Residuals:
>        Min         1Q     Median         3Q        Max
> -6.802e-17 -3.933e-17 -1.063e-17  1.807e-17  1.530e-16
>
> Coefficients:
>               Estimate Std. Error    t value Pr(>|t|)
> (Intercept)  1.099e+00  4.569e-17  2.404e+16   <2e-16 ***
> x           -1.275e-17  7.364e-18 -1.732e+00    0.122
> ---
> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
>
> Residual standard error: 6.688e-17 on 8 degrees of freedom Multiple R-
> squared: 0.5794, Adjusted R-squared: 0.5269
> F-statistic: 11.02 on 1 and 8 DF,  p-value: 0.01054
>
> How could this be possible?
> Did I missing something in my R code?
>
> Best,
> Miles
> --
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```

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