12.1 Introduction to 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. Photo by Joshua Rothhaas, CC BY 4.0.

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, the amount you pay a repair person for labor is often determined by an initial amount plus an hourly fee.

In this chapter, we will be studying the simplest form of regression, simple linear regression, with one independent variable [latex]x[/latex]. This involves data that fits a line in two dimensions. We will also study correlation which measures how strong the relationship is.

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