Chapter 12: Multiple Correlation and Multiple Regression
Student Resources
I use the 4 “P’s” framework to help you learn the material in this chapter: Prepare, Practice, Participate, and Perform. To increase the chances to succeed in this course, I strongly encourage you to complete all four “P’s” for each chapter.
1 Prepare
1.1 Chapter Overview
This chapter introduces multiple correlation and multiple regression—essential tools for modeling complex relationships with multiple predictors in Movement Science. You’ll learn how to extend bivariate regression to include multiple independent variables, interpret unstandardized and standardized coefficients, assess model fit using \(R^2\) and \(R^2_{\text{adj}}\), and understand the importance of checking for multicollinearity. We will focus primarily on Ordinary Least Squares (OLS) regression. For other selection methods and advanced techniques, please refer to Chapter 12 in the SMS textbook.
1.2 Multimedia Resources
The following table provides access to video and slide resources for this chapter. Click the links to open them in an overlay for better viewing on all devices.
| Resource | Description | Link |
|---|---|---|
| Long Video Overview | A detailed video explaining multiple correlation and multiple regression, interpreting coefficients, and diagnosing multicollinearity in movement science research. | 🔗 Watch Video |
| Slide Overview PDF | PDF slides that serve as an overview of this chapter. Read these before the textbook to introduce the main concepts and vocabulary. | 🔗 Download PDF |
| Slide Deck HTML | Interactive HTML slides for class. During class, the instructor controls the presentation; after class, review at your own pace. | 🔗 Open Slides |
| Slide Deck PDF | PDF version of the slide deck for download and offline viewing. | 🔗 Download PDF |
1.3 Read the Chapter
Read (Weir & Vincent, 2021, p. Ch.9) and (Furtado, 2026, p. Ch.12) to understand how to quantify relationships and predict outcomes using multiple predictors.
To succeed in this course, you must read the textbook chapters assigned for each topic. This is the only way to learn the material in depth.
Once done, proceed to the next section to practice what you learned.
2 Practice
Practicing what you learned in the chapter is essential to mastering the material. Below are some resources to help you practice the material in this chapter.
2.1 Frequently Asked Questions
Multiple regression models the relationship between a single continuous outcome variable and two or more predictor variables. It extends bivariate regression by estimating each predictor’s unique effect on the outcome, holding all other predictors constant.
\(R^2\) represents the proportion of variance in the outcome explained by the set of predictors, but it always increases when new predictors are added, even if they are irrelevant. Adjusted \(R^2\) corrects for this by penalizing the model for unnecessary predictors based on the sample size and number of predictors. It provides a more honest estimate of model fit.
A regression coefficient (\(b_i\)) represents the expected change in the outcome for a one-unit increase in the predictor, holding all other predictors constant. This isolating factor allows researchers to untangle unique contributions from multiple correlated variables.
Multicollinearity occurs when predictors in the model are highly intercorrelated. It makes it difficult for the regression model to attribute variance uniquely to each predictor, resulting in unstable coefficients, large standard errors, and potentially nonsignificant results for truly important predictors. We detect multicollinearity using the Variance Inflation Factor (VIF), with values > 10 indicating severe multicollinearity.
Partial correlation measures the relationship between two variables after removing the influence of other variables from both of them. It shows the “pure” relationship. Semipartial (part) correlation removes the influence of other predictors only from the predictor variable, not from the outcome. The square of the semipartial correlation equals the increase in \(R^2\) (\(\Delta R^2\)) when that predictor is added to the model.
No. Like bivariate regression, multiple regression only identifies associations. Even after controlling for potential confounders, unmeasured variables, reverse causation, or spurious relationships can still bias interpretations. Establishing causation requires rigorous experimental design.
2.2 Test your Knowledge
Take this low-stakes quiz to test your knowledge of the material in this chapter. This quiz is for practice only and will help you identify areas where you may need additional review.
3 Participate
This section includes activities and discussions that will be completed during class time. Your active participation is essential for deepening your understanding of the material.
During class, we will: - Build multiple OLS regression models using Movement Science datasets - Distinguish between shared and unique variance - Interpret unstandardized and standardized regression coefficients - Compute and verify \(R^2\) and Adjusted \(R^2\) - Evaluate multicollinearity using Variance Inflation Factors (VIF) - Practice reporting multiple regression results in APA format
4 Perform
4.1 Apply Your Learning
Now that you’ve prepared, practiced, and participated, it’s time to demonstrate your mastery of the material through assignments and assessments.
I strongly encourage you to complete the previous “Ps” (Prepare, Practice, Participate) before attempting any assignments or assessments associated with this chapter.