I am working with this data set:

u <- c(31,63,95,117,127,143,151.5,157)

v <- c(98.5,103.8,107.5,101,85,63,34.3,14)

I want to fit a model to these data so that u = f(v). 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?