Introduction

Chapter 4

Correlation and Linear Regression

Photo Credit: Forgiss / Crestock / Masterfile

Ethan J. Leib, the author of the book Friend v. Friend, believes that contemporary lifestyles are causing a decline in friendship. In an increasingly mobile society, are long-term friendships a thing of the past? Can you maintain a true friendship with over 1000 people on Facebook? What does being a friend really mean in the 21st century?

Oftentimes, when conducting a study or an experiment, a researcher is interested in knowing whether or not an association between two quantitative variables exists. For example, do people who retire earlier tend to live longer than those who work until an older age? Is there an association between a female’s annual salary and her education level? Is the number of minutes per day that a person spends on Facebook associated with the number of friends that he has? In this chapter we investigate quantitative bivariate data.

Bivariate data is that which has been collected by measuring two variables on each individual. Our goal will be to see if an association exists between a pair of quantitative variables and, if one does exist, to describe the association.

We begin by graphing quantitative bivariate data and determining the level and type of association (if any) that exist between the two variables. Association exists between bivariate data if a particular measurement for one variable is more likely to occur with certain other measurements of the other variable. If a linear association between the two variables does exist, we’ll see later in this chapter how to find a model to represent the relationship.