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

peter dalgaard pdalgd at gmail.com
Sat Sep 26 17:56:26 CEST 2015

```> On 26 Sep 2015, at 16:46 , Michael Eisenring <michael.eisenring at gmx.ch> wrote:
>
> 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

Sure I'm sure (& I did check!)... But notice that unlike R^2, Residual SE is not dimensionless. Switch from millimeters to meters in your response measure and the Residual SE instantly turns into 1.394. It's basically saying that your model claims to be able to predict Y within +/-2800 units. How good or bad that is, is your judgment.

> 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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>> and provide commented, minimal, self-contained, reproducible code.
>
> --
> Peter Dalgaard, Professor,
> Frederiksberg, Denmark
> Phone: (+45)38153501
> Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com
>
>
>
>
>
>
>
>

--
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com

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