Principal Components Regression in R (Step-by-Step)

However, when the predictor variables are highly correlated then multicollinearity can become a problem. This can cause the coefficient estimates of the model to be unreliable and have high variance. One way to avoid this problem is to instead use principal components regression, which finds M linear combinations (known as "principal components") of the original p predictors and then uses least squares to fit a linear regression model using the principal components as predictors. This tutorial provides a step-by-step example of how to perform principal components regression in R. The easiest way to perform principal components regression in R is by using functions from the pls package. For this example, we'll use the built-in R dataset called mtcars which contains data about various types of cars: For this example we'll fit a principal components regression (PCR) model using hp as the response variable and the following variables as the predictor variables: The following code shows how to fit the PCR model to this data.