Applying fitting data with nls

Question

Hi and thank you in advance for any suggestions here! My question is using nls() how can I

1. find the best optimal fit amongst the other fits-- ie linear and non linear-- for my data and

2. show the fit on the ggplot graph below?

   library(ggplot2)
   library(mosiac)
   library(tidyverse)
   library(dplyr)
   
   # data frame
   FX <- data.frame(Location=c(1:5), mi=c(1, 4, 16, 16^2,256^2))
   
   #Visual
   ggplot(FX,aes(x=Location, y=mi))+
     geom_line(alpha=0.9, color="red")
   
   # nls(). It shows error of Error in nls(mi ~ Location, data = FX, start = list(mi = 1, 
   #Location = 1)) : 
   #no parameters to fit
   nls(mi~Location,data=FX,start=list(mi=1,Location=1))
   

Answer 1

You need to include adjustable parameters for your equation in the nls() function.

FX <- data.frame(Location=c(1:5), mi=c(1, 4, 16, 16^2,256^2))

nls(mi~a+Location^b, data=FX, start=list(a=1, b=4))

# Nonlinear regression model
# model: mi ~ a + Location^b
# data: FX
# a         b 
# -3573.540     6.906 
# residual sum-of-squares: 142513083
# 
# Number of iterations to convergence: 8 
# Achieved convergence tolerance: 6.011e-06