Lesson 6.3: Multiple Linear Regression

Iain Pardoe

Lesson 6.3: Multiple Linear Regression

*“Multiplicity, My 1st” by Ojie Paloma is licensed under CC BY-NC-ND 2.0*

Lesson Learning Objectives

Use statistical software to fit the least squares multiple linear regression model.
Interpret and apply multiple linear regression models.

Lesson 6.3 Checklist

Learning activity	Graded?	Estimated time
Read OpenIntro Statistics section 9.1 and supplementary notes	No	30 mins
Watch instructional video	No	5 mins
Answer two section check-in questions	Yes	15 mins
Work through virtual statistical software lab	No	45 mins
Answer two virtual statistical software lab questions	Yes	15 mins
Work on practice exercises	No	1.5 hours
Explore suggested websites	No	15 mins
Complete and submit Unit 6 Assignment	Yes	2 hours
Work on the Practice Exam	No	3 hours
Complete and submit the Final Exam	Yes	3 hours

Learning Activities

Readings 📖 and Instructional Video 🎦

Introduction to Multiple Regression

Read Section 9.1: Introduction to Multiple Regression in OpenIntro Statistics (Diez et al., 2019) CC BY-SA 3.0. This lesson builds on Lesson 6.2 by introducing multiple linear regression, a model with multiple predictor variables (x₁, x₂, …) used to predict a single numerical response variable (y). The predictor variables can be a mix of numerical and categorical variables, so the model is extremely flexible. As you read, look up new terminology in the Glossary and self-assess your understanding by attempting the guided practice exercises.

Watch the following video, Introduction to Multiple Regression (Barr et al., 2013), on multiple linear regression (duration 00:04:52).

Multiple Linear Regression

Read Supplementary Notes 6.3, which summarizes what you need to know about multiple linear regression for this course.

Lesson Check-in Questions ✍

Answer the two check-in questions for Lesson 6.3 in your Moodle course. The questions are based on the material covered in the readings and instructional videos. The questions are multiple-choice, fill-in-the-blank, matching, or calculation questions, and they are auto-graded in Moodle. Once you access the questions, you have 15 minutes to submit your answers. Overall the Lesson Check-in Questions count 6% toward your total grade.

Virtual Statistical Software Lab 💻

Work through the virtual statistical software lab: Software Lab 6.3. In this lab you’ll analyze a multiple linear regression model for the professor evaluation score data from Software Lab 6.1. As you work through the lab, answer the exercises in the shaded boxes. These exercises are not graded but the solutions are available: Software Lab 6.3 Solutions. The lab should take you no more than 45 minutes to complete.

Virtual Statistical Software Lab Questions ✍

Answer the two virtual statistical software lab questions for Software Lab 6.3 in your Moodle course. The questions are based on the lab you just completed. The questions are multiple-choice, fill-in-the-blank, matching, or calculation questions, and they are auto-graded in Moodle. Once you access the questions, you have 15 minutes to submit your answers. Overall the Software Lab Questions count 6% toward your total grade.

Practice Exercises 🖊

Work on the following exercises in OpenIntro Statistics: Exercises 9.1 and 9.3, and Chapter Exercise 9.19 (Diez et al., 2019) CC BY-SA 3.0. Check your answers using these solutions (Diez et al., 2019) CC BY-SA 3.0. You’ll deepen your understanding much more effectively if you genuinely attempt the questions by yourself before checking the solutions.

Work on the WeBWorK exercises, which are linked from your Moodle course. Check your answers using the solutions provided.

Suggested Websites 🌎

For another take on multiple linear regression, have a look at this well-written online resource: Multiple Linear Regression – A Quick Guide (Examples) (Bevans, 2023).
If you want to go a little more in-depth and get a sense for the power of the statistical software R (on which jamovi is built), check-out this great online tutorial: Multiple Linear Regression Made Simple (Soetewey, 2021).

Unit Assignment ✍

Having completed the three lessons in this unit, you should now do the Unit 6 Assignment in your Moodle course, which counts 6% towards your overall grade. There are five questions—a mix of short-answer, multiple-choice, and calculation questions—and you submit your answers directly in Moodle. There is no time limit for completing the assignment, and you do not have to complete it in one sitting. Three of the questions will be auto-graded in Moodle, and two will be manually graded by your Open Learning Faculty Member. You are recommended to submit this assignment before you start to prepare for the Final Exam. That way you can benefit from your Open Learning Faculty Member’s feedback.

Practice Exam 🖊

Having completed all six units, all that remains is the Final Exam, which counts 40% towards your overall grade. To help you prepare for the Final Exam, there is a Practice Exam available in your Moodle course. The Practice Exam has the same structure and covers similar topics as the Final Exam. There are ten questions based on Units 1–6: a mix of short-answer, multiple-choice, fill-in-the-blank, matching, and calculation questions. You will submit your answers directly in the Practice Exam in Moodle. You are recommended to take the Practice Exam under exam conditions and with a 3-hour time limit. Some questions will be partly auto-graded in Moodle, while solutions are provided for the other questions to allow you to self-check your answers. The Practice Exam is not graded by your Open Learning Faculty Member.

Final Exam ✍

Your mandatory, invigilated Final Exam counts 40% towards your overall grade. Review the instructions in the Course Guide to apply to take the Final Exam. The Final Exam has ten questions based on Units 1–6: a mix of short-answer, multiple-choice, fill-in-the-blank, matching, and calculation questions. There is a 3-hour time limit for completing the Final Exam. The questions will be partly auto-graded in Moodle, and partly manually graded by your Open Learning Faculty Member. Use your lesson check-in questions, software lab questions, unit assignments, Midterm Exam, and the Practice Exam to prepare for the Final Exam.

Media Attributions

Multiplicity, My 1st, by Ojie Paloma (2009), on Flickr, CC BY-NC-ND 2.0

References

Barr, C., Rico, J., & Diez, D. [OpenIntroOrg]. (2013, Nov. 13). Introduction to multiple regression [Video]. YouTube. https://www.youtube.com/watch?v=sQpAuyfEYZg

Bevans, R. (2020, Feb. 20). Multiple linear regression | A quick guide (Examples). Scribbr. https://www.scribbr.com/statistics/multiple-linear-regression/

Diez, D. M., Çetinkaya-Rundel, M., Barr, C. D. (2019). OpenIntro Statistics (4^th ed.). OpenIntro. https://www.openintro.org/book/os/

Paloma, O. (2008). Multiplicity, my 1st [Photograph]. Flickr. https://flic.kr/p/5REdUg

Soetewey, A. (2021, Oct. 4). Multiple linear regression made simple. Stats and R. https://statsandr.com/blog/multiple-linear-regression-made-simple/

License

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Introduction to Probability and Statistics Copyright © 2023 by Thompson Rivers University is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.