*61*

**Polynomial regression** is a regression technique we use when the relationship between a predictor variable and a response variable is nonlinear.

This tutorial explains how to plot a polynomial regression curve in R.

**Related:**Â The 7 Most Common Types of Regression

**Example: Plot Polynomial Regression Curve in R**

The following code shows how to fit a polynomial regression model to a dataset and then plot the polynomial regression curve over the raw data in a scatterplot:

#define data x #plot x vs. y plot(x, y, pch=16, cex=1.5) #fit polynomial regression model fit #use model to get predicted values pred return=T)$ix #add polynomial curve to plot lines(x[ix], pred[ix], col='red', lwd=2)

We can also add the fitted polynomial regression equation to the plot using the **text()** function:

#define data x #plot x vs. y plot(x, y, pch=16, cex=1.5) #fit polynomial regression model fit #use model to get predicted values pred return=T)$ix #add polynomial curve to plot lines(x[ix], pred[ix], col='red', lwd=2) #get model coefficients coeff #add fitted model equation to plot text(9, 200 , paste("Model: ", coeff[1], " + ", coeff[2], "*x", "+", coeff[3], "*x^2", "+", coeff[4], "*x^3"), cex=1.3)

Note that the **cex** argument controls the font size of the text. The default value is 1, so we chose to use a value of **1.3** to make the text easier to read.

**Additional Resources**

An Introduction to Polynomial Regression

How to Fit a Polynomial Curve in Excel

How to Perform Polynomial Regression in Python