如何在 R 中绘制 inc 指数衰减？

Question

My prof decided that our first experience with coding was going to be trying to fit the function z(t) = A(1-e^(-t/T)) into a given data-set from class using R. I'm completely lost. I keep using lm and nls functions, without quite knowing how they work. So far, I have the data graphed but I have no clue how to get any sort of line more complicated than

mod3<-lm(y~I(x^1/5))
pre3<-predict(mod3)
lines(pre3)

to sum up: how do I find the A and T parameters? Do I use nls for the formula? Anything helps. I'll include a picture of the graph and the data. Please ignore the random lines on the plot. graph depicting my dataset dataset I have to use

Answer 1

One could attempt transform your expression into a linear relationship, but sometimes it is easier to just let the computer do the work. As mention in the comments, R has the nls function to perform the nonlinear regression.

Here is an example using some dummy data. The supply the nls function with your equation, the data frame containing the data and supply it with the initial estimates of the parameters.

See comments for additional details.

#create dummy data
A= 0.8
T1 = 13

t <- seq(2, 50, 3)
z <- A*(1-exp(-t/T1)) 
z<- z +rnorm(length(z), 0, 0.005) #add noise

#starting data frame
df <-data.frame(t, z)

#solve non-linear model
model <- nls(z ~ A*(1-exp(-t/Tc)), data=df, start = list(A=1, Tc=1))
print(summary(model))
#predict
pred_y <-predict(model, data.frame(t))

#plot
plot(x=t, y=z)
lines(y=pred_y, x= t, col="blue")