# [R] how to get r-squared for a predefined curve or function with "other" data points

protoplast nolf.markus at gmail.com
Thu Feb 16 17:43:08 CET 2012

```hello mailing list!
i still consider myself an R beginner, so please bear with me if my
questions seems strange.

i'm in the field of biology, and have done consecutive hydraulic
conductivity measurements in three parallels ("Sample"), resulting in three
sets of conductivity values ("PLC" for percent loss of conductivity,
relative to 100%) at multiple pressures ("MPa").

---
Sample      MPa    PLC
1      -0.3498324    0.000000
1      -1.2414770   15.207821
1      -1.7993249   23.819995
1      -3.0162866   33.598570
1      -3.5184321   46.376933
1      -3.9899791   67.532226
1      -4.2731145   89.735541
1      -4.7597244   99.836239
2      -0.2754036    0.000000
2      -1.2912619   12.476132
2      -1.5128974   13.543273
...
---

since each sample is a statistical unit, i have fitted each sample-subset to
a sigmoid curve:

---
plot(
NA,
NA,
main="",
xlim=c(-20,0),
ylim=c(0,100),
xlab = "water potential [MPa]",
ylab = "percent loss of conductivity [%]",
xaxp = c(0,-20,4),
yaxp = c(0,100,5),
tck = 0.02,
mgp = c(1.5,0.1,0),
)

for(i in 1:3){
x <- subset(curvedata,Group == i)\$MPa
y <- subset(curvedata,Group == i)\$PLC
name <- subset(curvedata,Group == i)\$Sample
points(x,y)

vlc <- nls(y ~ 100/(1+exp(a*(x-b))), start=c(a=1, b=-3), data=list(x,y))

Rsquared <- 1 - var(residuals(vlc))/var(y)

summarizeall[i ,"Run"] <- i
summarizeall[i ,"Sample"] <- name[1]
summarizeall[i ,"a"] <- coef(vlc)[1]
summarizeall[i ,"b"] <- coef(vlc)[2]
summarizeall[i ,"R2"] <- Rsquared

listnow <- data.frame(list(Run = c(i),Sample = c(name[1]), a =
c(coef(vlc)[1]), b = c(coef(vlc)[2]), R2 = c(Rsquared)))
print(listnow)

i <- i+1
}
---

...and get three slightly different curves with three different estimatinos
of fit (r², Rsquared).

---
> summarizeall
Sample   a       b        R2
1   1 1.388352 -3.277755 0.9379886
2   2 1.800007 -3.363075 0.9327164
3   3 1.736857 -2.743972 0.9882998

> average
Var n     a          b         R2
1 Mean 3 1.6417389 -3.1282673 NA
2   SE . 0.1279981  0.1937197 NA
---

by averaging parameters a and b of the curve, i create a "mean curve" that
is added to the plot (red curve in the attached image).

http://r.789695.n4.nabble.com/file/n4394609/conductivity-curve.gif

---
meana <- average[1,"a"]
meanb <- average[1,"b"]
curve(100/(1+exp(meana*(x-meanb))), col=2, lwd=2, add = TRUE)
---

and now here's my problem:
i'd like to calculate R squared for all points on that mean curve.
since i have to average the curve parameters, i loose the curve's residuals
that are stored in my variable vlc (the result of the nls function) for
every sample.
just fitting one curve to all the data points is not good enough.

an extensive google search over several days hasn't gotten me anywhere, but
maybe someone here can help me?

is there an efficient way to calculate r squared for a predefined function
with "unrelated" data points?
(unrelated as in "not used directly for fitting")