Chapter 8 Linear relationships

Up until now we’ve been dealing almost exclusively with categorical variables in some way. For example, chi-square tests are for testing relationships between categorical variables; likewise, t-tests and ANOVAs deal with categorical IVs against continuous DVs. In reality though, many of the things we’re interested in are inherently continuous in nature. There are very few psychological constructs that aren’t continuous in some way, and so working with continuous variables forms a core part of doing statistical analyses.

Enter the linear regression and its many other forms - in some ways, the bedrock of many of the research that we do (more on this in Week 11). When we’re dealing with continuous variables, linear regressions are generally the first place to start. We won’t go much further beyond the basics here (certainly as it applies to a lot of psychological research), but even these concepts are foundational for many reasons.

By the end of this module you should be able to:

• Describe how hypothesis testing works in regressions - including what is being tested
• Conduct appropriate assumption tests for a linear regression
• Run a linear regression and interpret the output
• Make predictions based on the output of a linear regression
• Run and interpret a multiple regression

Figure 8.1: xkcd: Linear Regression