# [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 07:08:52 CEST 2015

```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

dta<-read.csv("Regression_exp2.csv",header=T, sep = ",")
attach(dta)      # tells R to do the following analyses on this dataset
head(dta)

# loading packages: analysis of mixed effect models
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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