# MA251: Statistics II

Unit 3: Model Building with Multiple Regression   This unit will provide you with a framework for building and evaluating regression models. You will learn how to select regression models using automatic procedures such as forward selection and backward elimination. You will also learn to use diagnostic tools to evaluate the accuracy of a regression model and to measure effects of multicollinearity.

This unit will take you approximately 20 hours to complete.

☐    Subunit 3.1: 10 hours

☐    Subunit 3.2: 4 hours

☐    Subunit 3.3: 6 hours

Unit3 Learning Outcomes
Upon successful completion of this unit, the student will be able to:

• perform selection of multiple regression models using forward selection, backward elimination, and stepwise selection procedures;
• diagnose performance of a multiple regression;
• explain and quantify multicollinearity; and
• perform corrective actions to reduce the effects of multicollinearity.

3.1 Model Selection Procedures   - Reading: University of Florida: Alan Agresti’s Statistical Methods for the Social Sciences II: “Chapter 14: Model Building with Multiple Regression” The Saylor Foundation does not yet have materials for this portion of the course. If you are interested in contributing your content to fill this gap or aware of a resource that could be used here, please submit it here.

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• Reading: Jeff Miller and Patricia Haden’s Statistical Analysis with the General Linear Model: “Chapter 17: Finding the Best Model” Link: Jeff Miller and Patricia Haden’s Statistical Analysis with the General Linear Model: “Chapter 17: Finding the Best Model” (PDF)

Instructions: Click on the link “Download the book as a PDF file” to save and download the textbook. You will use this textbook throughout the course. Read “Chapter 17: Finding the Best Model,” which will provide an overview of best practices for selecting models. You will also learn how to use automatic model selection procedures, including forward selection, backward elimination, and stepwise procedures.

Reading this chapter should take approximately 4 hours.

• Assessment: University of Chicago: Robert Brandon Gramacy’s “Applied Regression Analysis: Homework 6” Link: University of Chicago: Robert Brandon Gramacy’s “Applied Regression Analysis: Homework 6” (PDF)

Instructions: Click on the link above, which will take you to the website of BUS 41100. Scroll down to Homework 6 and complete all problems in the homework. Follow the instructions for the problems closely. The solutions to the homework are in the R code. The comments in the R code are helpful for understanding the results.

Completing this assessment should take approximately 4 hours.

3.2 Regression Diagnostics   - Reading: University of Florida: Alan Agresti’s Statistical Methods for the Social Sciences II: “Chapter 14: Model Building with Multiple Regression” The Saylor Foundation does not yet have materials for this portion of the course. If you are interested in contributing your content to fill this gap or aware of a resource that could be used here, please submit it here.

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3.3 Effects of Multicollinearity   - Reading: University of Florida: Alan Agresti’s Statistical Methods for the Social Sciences II: “Chapter 14: Model Building with Multiple Regression” The Saylor Foundation does not yet have materials for this portion of the course. If you are interested in contributing your content to fill this gap or aware of a resource that could be used here, please submit it here.

``````[Submit Materials](/contribute/)
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• Web Media: YouTube: How2Stats’ “Multicollinearity—Explained Simply (part 1)” and “Multicollinearity—Explained Simply (part 2)” Link: YouTube: How2Stats’ “Multicollinearity—Explained Simply (part 1)” and “Multicollinearity—Explained Simply (part 2)” (YouTube)

Instructions: Watch the two videos, which will give an overview of the effects of multicollinearity on variance as well as methods to measure multicollinearity, including tolerance and variance inflation factor (VIF). What happens when VIF exceeds 10? What can you do to correct for multicollinearity?

Watching the two videos should take approximately 15 minutes.

• Assessment: University of Chicago: Robert Brandon Gramacy’s “Applied Regression Analysis: Homework 7” Link: University of Chicago: Robert Brandon Gramacy’s “Applied Regression Analysis: Homework 7” (PDF)

Instructions: Click on the link above, which will take you to the website of BUS 41100. Select Homework 7 and complete all problems in the assignment. Follow the instructions for the problems closely. The solutions to the homework are in the R code. The comments in the R code are helpful for understanding the results.

Completing this assessment should take approximately 5 hours.