[R] Using R to fit a curve to a dataset using a specific equation

[David L Carlson]

I can get you started, but you should really read up on non-linear least squares. Calling your data frame dta (since data is a function):

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, length.out=200)
lines(xval, predict(dta.nls, data.frame(Damage_cm=xval)))
profile(dta.nls, alpha= .05)
===========================================
Number of iterations to convergence: 3 
Achieved convergence tolerance: 1.750586e-06
attr(,"summary")

Formula: Gossypol ~ y0 + a * (1 - b^Damage_cm)

Parameters:
       Estimate   Std. Error t value   Pr(>|t|)    
y0 1303.4529432  386.1515684 3.37550  0.0013853 ** 
a  2796.0464520  530.4140959 5.27144 2.5359e-06 ***
b     0.4939111    0.1809687 2.72926  0.0085950 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1394.375 on 53 degrees of freedom

Number of iterations to convergence: 3 
Achieved convergence tolerance: 1.750586e-06


David Carlson
Dept of Anthropology
Texas A&M
College Station, TX  77843
________________________________________
From: R-help [r-help-bounces at r-project.org] on behalf of Michael Eisenring [michael.eisenring at gmx.ch]
Sent: Saturday, August 01, 2015 10:17 AM
To: r-help at r-project.org
Subject: [R] Using R to fit a curve to a dataset using a specific equation

Hi there




I would like to use a specific equation to fit a curve to one of my data
sets (attached)

> dput(data)

structure(list(Gossypol = c(1036.331811, 4171.427741, 6039.995102,
5909.068158, 4140.242559, 4854.985845, 6982.035521, 6132.876396,
948.2418407, 3618.448997, 3130.376482, 5113.942098, 1180.171957,
1500.863038, 4576.787021, 5629.979049, 3378.151945, 3589.187889,
2508.417927, 1989.576826, 5972.926124, 2867.610671, 450.7205451, 1120.955,
3470.09352, 3575.043632, 2952.931863, 349.0864019, 1013.807628, 910.8879471,
3743.331903, 3350.203452, 592.3403778, 1517.045807, 1504.491931,
3736.144027, 2818.419785, 723.885643, 1782.864308, 1414.161257, 3723.629772,
3747.076592, 2005.919344, 4198.569251, 2228.522959, 3322.115942,
4274.324792, 720.9785449, 2874.651764, 2287.228752, 5654.858696,
1247.806111, 1247.806111, 2547.326207, 2608.716056, 1079.846532), Treatment
= structure(c(2L, 3L, 4L, 5L, 2L, 3L, 4L, 5L, 1L, 2L, 3L, 5L, 1L, 2L, 3L,
4L, 5L, 1L, 2L, 3L, 4L, 5L, 1L, 2L, 3L, 4L, 5L, 1L, 2L, 3L, 4L, 5L, 1L, 2L,
3L, 4L, 5L, 1L, 2L, 3L, 4L, 5L, 1L, 2L, 3L, 4L, 5L, 1L, 2L, 3L, 4L, 5L, 1L,
2L, 3L, 1L), .Label = c("C", "1c_2d", "3c_2d", "9c_2d", "1c_7d"), class =
"factor"), Damage_cm = c(0.4955, 1.516, 4.409, 3.2665, 0.491, 2.3035, 3.51,
1.8115, 0, 0.4435, 1.573, 1.8595, 0, 0.142, 2.171, 4.023, 4.9835, 0, 0.6925,
1.989, 5.683, 3.547, 0, 0.756, 2.129, 9.437, 3.211, 0, 0.578, 2.966, 4.7245,
1.8185, 0, 1.0475, 1.62, 5.568, 9.7455, 0, 0.8295, 2.411, 7.272, 4.516, 0,
0.4035, 2.974, 8.043, 4.809, 0, 0.6965, 1.313, 5.681, 3.474, 0, 0.5895,
2.559, 0)), .Names = c("Gossypol", "Treatment", "Damage_cm"), row.names =
c(NA, -56L), class = "data.frame")

The equation is: y~yo+a*(1-b^x) Where: 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

In the end I would like to use the equation to plot a curve (with SE
interval, I usually use ggplot2)

Furthermore, I would like to know the R2 and p value. I would also be
interested in the parameters yo , a and b

I have never done this before and would be extremely grateful if anyone
could help me? I suppose I have to use a non linear approach (glm(...)). I
found out that the mosaic package might be helpful.

thanks a lot, Mike




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