rcurve-fittingdata-analysispolynomial-math

Fitting polynomial model to data in R


I've read the answers to this question and they are quite helpful, but I need help.

I have an example data set in R as follows:

x <- c(32,64,96,118,126,144,152.5,158)  
y <- c(99.5,104.8,108.5,100,86,64,35.3,15)

I want to fit a model to these data so that y = f(x). I want it to be a 3rd order polynomial model.

How can I do that in R?

Additionally, can R help me to find the best fitting model?


Solution

  • To get a third order polynomial in x (x^3), you can do

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

    or

    lm(y ~ poly(x, 3, raw=TRUE))
    

    You could fit a 10th order polynomial and get a near-perfect fit, but should you?

    EDIT: poly(x, 3) is probably a better choice (see @hadley below).