Introduction: Linear Regression and Correlation

This is a photo of a car mechanic’s shop. There are three United States Postal Services trucks being serviced, and one not being serviced.
Linear regression and correlation can help you determine if an auto mechanic’s salary is related to his work experience. (credit: Joshua Rothhaas)

Learning Objectives

By the end of this chapter, the student should be able to:

  • Discuss basic ideas of linear regression and correlation.
  • Create and interpret a line of best fit.
  • Calculate and interpret the correlation coefficient.
  • Calculate and interpret outliers.

Professionals often want to know how two or more numeric variables are related. For example, is there a relationship between the grade on the second math exam a student takes and the grade on the final exam? If there is a relationship, what is the relationship and how strong is it?

In another example, your income may be determined by your education, your profession, your years of experience, and your ability. The amount you pay a repair person for labor is often determined by an initial amount plus an hourly fee.

The type of data described in the examples is bivariate data — “bi” for two variables. In reality, statisticians use multivariate data, meaning many variables.

In this chapter, you will be studying the simplest form of regression, “linear regression” with one independent variable (x). This involves data that fits a line in two dimensions. You will also study correlation which measures how strong the relationship is.