# [R] How to calculate standard error of estimate (S) for my non-linear regression model?

Michael Eisenring michael.eisenring at gmx.ch
Sat Sep 26 16:46:01 CEST 2015

```Dear Peter,
If I look at my summary I see there a Residual standard error: 1394 on 53
degrees of freedom.
This number is very high (the fit of the curve is pretty bad I know but
still...). Are you sure the residual standard error given in the summary is
http://onlinestatbook.com/2/regression/accuracy.html
I am basically just looking for a value that describes the goodness of fit
for my non-linear regression model.

This is probably a pretty obvious question, but I am not a statistician and
as you said the terminology is sometimes pretty confusing.
Thanks mike

-----Ursprüngliche Nachricht-----
Von: peter dalgaard [mailto:pdalgd at gmail.com]
Gesendet: Samstag, 26. September 2015 01:43
An: Michael Eisenring <michael.eisenring at gmx.ch>
Cc: r-help at r-project.org
Betreff: Re: [R] How to calculate standard error of estimate (S) for my
non-linear regression model?

This is one area in which terminology in (computational) statistics has gone
a bit crazy. The thing some call "standard error of estimate" is actually
the residual standard deviation in the regression model, not to be confused
with the standard errors that are associated with parameter estimates. In
summary(nls(...)) (and summary(lm()) for that matter), you'll find it as
"residual standard error",  and even that is a bit of a misnomer.

-pd

> On 26 Sep 2015, at 07:08 , Michael Eisenring <michael.eisenring at gmx.ch>
wrote:
>
> Hi all,
>
> I am looking for something that indicates the goodness of fit for my
> non linear regression model (since R2 is not very reliable).
>
> I read that the standard error of estimate (also known as standard
> error of the regression) is a good alternative.
>
>
>
> The standard error of estimate is described on this page (including
> the
> formula) http://onlinestatbook.com/2/regression/accuracy.html
> <https://3c.gmx.net/mail/client/dereferrer?redirectUrl=http%3A%2F%2Fon
> linest atbook.com%2F2%2Fregression%2Faccuracy.html>
>
> Unfortunately however, I have no clue how to programm it in R. Does
> anyone know and could help me?
>
> Thank you very much.
>
>
>
> I added an example of my model and a dput() of my data
>
> #CODE
>
> attach(dta)      # tells R to do the following analyses on this dataset
>
>
>
> library(nls2)#model
>
> #Aim: fit equation to data: y~yo+a*(1-b^x) : Two parameter exp. single
> rise to the maximum # y =Gossypol (from my data set) x= Damage_cm
> (from my data set) #The other 3 parameters are unknown: yo=Intercept,
> a= assymptote ans b=slope
>
> plot(Gossypol~Damage_cm, dta)
> # Looking at the plot, 0 is a plausible estimate for y0:
> # a+y0 is the asymptote, so estimate about 4000; # b is between 0 and
> 1, so estimate .5 dta.nls <- nls(Gossypol~y0+a*(1-b^Damage_cm), dta,
>               start=list(y0=0, a=4000, b=.5))
>
> xval <- seq(0, 10, 0.1)
> lines(xval, predict(dta.nls, data.frame(Damage_cm=xval)))
> profile(dta.nls, alpha= .05)
>
>
> summary(dta.nls)
>
>
>
>
>
>
>
> #INPUT
>
> structure(list(Gossypol = c(948.2418407, 1180.171957, 3589.187889,
> 450.7205451, 349.0864019, 592.3403778, 723.885643, 2005.919344,
> 720.9785449, 1247.806111, 1079.846532, 1500.863038, 4198.569251,
> 3618.448997, 4140.242559, 1036.331811, 1013.807628, 2547.326207,
> 2508.417927, 2874.651764, 1120.955, 1782.864308, 1517.045807,
> 2287.228752, 4171.427741, 3130.376482, 1504.491931, 6132.876396,
> 3350.203452, 5113.942098, 1989.576826, 3470.09352, 4576.787021,
> 4854.985845, 1414.161257, 2608.716056, 910.8879471, 2228.522959,
> 2952.931863, 5909.068158, 1247.806111, 6982.035521, 2867.610671,
> 5629.979049, 6039.995102, 3747.076592, 3743.331903, 4274.324792,
> 3378.151945, 3736.144027, 5654.858696, 5972.926124, 3723.629772,
> 3322.115942, 3575.043632, 2818.419785), Treatment = structure(c(5L,
> 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
> 1L, 1L, 1L, 1L, 1L, 3L, 3L, 3L, 3L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L,
> 3L, 3L, 3L, 2L, 2L, 2L, 4L, 2L, 4L, 4L, 2L, 4L, 2L, 2L, 4L, 4L, 4L,
> 4L, 4L, 4L, 2L), .Label = c("1c_2d", "1c_7d", "3c_2d", "9c_2d", "C"),
> class = "factor"), Damage_cm = c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
> 0.142, 0.4035, 0.4435, 0.491, 0.4955, 0.578, 0.5895, 0.6925, 0.6965,
> 0.756, 0.8295, 1.0475, 1.313, 1.516, 1.573, 1.62, 1.8115, 1.8185,
> 1.8595, 1.989, 2.129, 2.171, 2.3035, 2.411, 2.559, 2.966, 2.974,
> 3.211, 3.2665, 3.474, 3.51, 3.547, 4.023, 4.409, 4.516, 4.7245, 4.809,
> 4.9835, 5.568, 5.681, 5.683, 7.272, 8.043, 9.437, 9.7455),
> Damage_groups = c(0.278, 1.616, 2.501, 3.401, 4.577, 5.644, 7.272,
> 8.043, 9.591, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA),
> Gossypol_Averaged = c(1783.211, 3244.129, 2866.307, 3991.809,
> 4468.809, 5121.309, 3723.629772, 3322.115942, 3196.731, NA, NA, NA,
> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA), Groups = c(42006L, 42038L,
> 42067L, 42099L, 42130L, 42162L, 42193L, 42225L, 42257L, NA, NA, NA,
> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA)), .Names = c("Gossypol",
> "Treatment", "Damage_cm", "Damage_groups", "Gossypol_Averaged",
> "Groups"), class = "data.frame", row.names = c(NA, -56L))
>
>
>
>
> 	[[alternative HTML version deleted]]
>
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--
Peter Dalgaard, Professor,