R – NonLinear Least Square
Non-Linear Least Square
Mathematical Formula:
where,
r is residual or error value between 2 points.
resid()
Syntax:
nls(formula, start)
where,
formula indicates the model formula i.e., non-linear function start is a list of starting estimates
Note: To know about more optional parameters of nls(), use below command in R console –
help("nls")
Example 1 :
# defining x and y coordinates x <- seq(0, 10, 0.1) y <- rnorm(101, 5, 1) # output to be present as PNG file png(file ="nls.png") # Taking the model to get fitted m <- nls(y~a * x ^ 3 + b * x + c, start = list(a = 1, b = 2, c = 1)) # plot the graph plot(x, y, col.lab ="darkgreen", col.axis ="darkgreen") # plot the graph with new fitting line # or regression line lines(x, predict(m)) # saving the file dev.off() # print minimum residual or error value print(sum(resid(m)^2)) |
Output :
[1] 106.4507
Example 2 :
cor()
# creating sequence of 101 values from 0 to 100 x <- seq(0, 100, 1) y<-((runif(1, 10, 20)*x)/(runif(1, 0, 10) + x)) + rnorm(101, 0, 1) # output to be present as PNG file png(file ="nls2.png") # using starting values in nls() function # to not get a warning m<-nls(y~a * x/(b + x), start = list(a = 1, b = 2)) # goodness of fit cor(y, predict(m)) # minimized residual value sum(resid(m)^2) # plotting points on graph plot(x, y) # finding regression line lines(x, predict(m)) # saving the file dev.off() |
Output :
[1] 0.9622681 [1] 108.1481