x <- 1:20
y <- 3*x^2+ 30*rnorm(20)
plot(x,y)
fit <- nls(y ~ a*x^b, start = list(a=2, b= 1.5))
lines(seq(1, 20, by = 0.1), predict(fit, data.frame(x=seq(1, 20, by = 0.1))))
fit
Nonlinear regression model
model: y ~ a * x^b
data: parent.frame()
a b
3.366 1.963
residual sum-of-squares: 16158
Number of iterations to convergence: 6
Achieved convergence tolerance: 4.238e-07