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

peter dalgaard pdalgd at gmail.com
Sat Sep 26 10:42:44 CEST 2015

```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%2Fonlinest
> 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))
>
>
>
>
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>
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