Sigmoidal Curve Fit in R [duplicate]

Question

I'm a beginner to R and I'm trying to fit a curve onto a data set that (for example) might look like the below:

(x- value)  (y-value)
105 423
115 471
125 567
135 808
145 921.5
155 1040

The x value's represent the amount of stimulus and the y values represent motor responses (in uV). These are averages over 10 subjects, where the x-values are the same for each subject.

I was told that this data set normally follows a sigmoidal fit. I tried fitting it with the following:

fit <- lm( y ~ poly(x, 3) )

But I'm not sure if this is the appropriate way to do this :(

My code looks like this so far:

p <- ggplot (data, aes(x, y)) +
  geom_point(shape= 21, fill= "blue", colour= "black", size=2) +
  xlab("X value") + ylab("Y value") +
  geom_smooth(method= "lm", se= FALSE,  colour= "red", formula=y ~ poly(x, 3, raw=TRUE)) +
  geom_errorbar(aes(ymin=y-SE, ymax=y+SE), width=.9)+ 
  ggtitle ("Title")
p

Additionally: Once I fit the the curve I would also like to obtain the slope (calculated as the value of the tangent at the steepest point of the curve)

Thanks in advance, any help would be greatly appreciated!

Answer 1

I don't know how the poly() function is supposed to work but if you want a 3rd order polynomial fit just use:

   lm1=lm(y~I(x^3)+I(x^2)+x)

That makes a pretty good fit on your toy data above. For the slope at the inflection point. I would set the second derivative to zero and solve for x. Then compute the first dirivative at that x.

But I think you would prefer a logistic growth model.