Fitting a polynomial regression model with lm

Some predictor variables and response variables may have a non-linear relationship, and their relationship can be modeled as an n^th order polynomial. In this recipe, we will introduce how to deal with polynomial regression using the lm and poly functions.

Getting ready

Prepare the dataset that includes a relationship between the predictor and response variable that can be modeled as an n^th order polynomial. In this recipe, we will continue to use the Quartet dataset from the car package.

How to do it...

Perform the following steps to fit the polynomial regression model with lm:

1. First, we make a scatter plot of the x and y2 variables:

        > plot(Quartet$x, Quartet$y2)  

Scatter plot of variables x and y2

2. You can apply the poly function by specifying 2 in the argument:

        > lmfit = lm(Quartet$y2~poly(Quartet$x,2))
        > lines(sort(Quartet$x), lmfit$fit[order(Quartet$x)], col = "red")  

A quardratic fit example of the regression plot...