# MA251: Statistics II

Unit 2: Multiple Regression and Correlation   The term “multiple regression” was first introduced by Pearson in 1908. Since then, multiple regression has evolved to be a powerful statistical technique used in all fields of research, ranging from biology, sociology, psychology, to engineering. Multiple regression enables you to learn about the relationship between several independent or predictor variables and one dependent variable. For instance, multiple regression has been used to understand how housing price depends on location, the size (in square feet), the number of bedrooms, the number of bathrooms, the architecture style, the average income of the respective neighborhood, the crime statistics, and so forth. In this unit, you will learn several fundamental concepts of multiple regression, including R2 and partial correlation. You also will learn to perform and interpret results of multiple regression.

This unit will take you approximately 24 hours to complete.

☐    Subunit 2.1: 9 hours

☐    Subunit 2.2: 2 hours

☐    Subunit 2.3: 2 hours

☐    Subunit 2.4: 5 hours

☐    Subunit 2.5: 6 hours

Unit2 Learning Outcomes
Upon successful completion of this unit, the student will be able to:

• perform multiple regression on numerical and categorical variables;
• explain the significance of R2;
• perform inference for multiple regression and coefficients; and
• evaluate partial correlation.

2.1 Introduction to Multiple Regression   - Lecture: YouTube: EconDrD’s “Multiple Regression Lecture Notes 1” Link: YouTube: EconDrD’s “Multiple Regression Lecture Notes 1” (YouTube)

Instructions: Click on the link for “Multiple Regression Lecture Notes 1”. The video will introduce you to multiple regression.

`````` Watching this video and pausing to take notes should take
approximately 30 minutes.

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• Reading: Jeff Miller and Patricia Haden’s Statistical Analysis with the General Linear Model: “Chapter 14: Multiple Regression” Link: Jeff Miller and Patricia Haden’s Statistical Analysis with the General Linear Model: “Chapter 14: Multiple Regression” (PDF)

Instructions: Click on the link “Download the book as a PDF file” to download and save the textbook. You will use this textbook throughout the course. For many problems, it is unreasonable to expect that there is only one independent variable that influences the behavior of the dependent variable. Multiple regression is designed to address this type of problem. What are the basic steps of multiple regression? Compare these steps to linear regression.

Reading this chapter should take approximately 3 hours.

• Reading: University of Florida: Alan Agresti’s Statistical Methods for the Social Sciences II: “Chapter 11: Multiple Regression and Correlation” 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

Instructions: Click on the link for “Multiple regression dummy variables”. The lecture will introduce you to multiple regression for categorical and qualitative variables. Sometimes we want to include a categorical variable (e.g., gender or education level) in our model. These types of variables can be represented by dummy variables – variables with only two values, 0 and 1. The number of dummy variables for each categorical variable is k-1, where k is the number of levels of the original variable.

Watching this video and pausing to take notes should take approximately 30 minutes.

• Assessment: University of Chicago: Robert Brandon Gramacy’s “Applied Regression Analysis: Homework 5” Link: University of Chicago: Robert Brandon Gramacy’s “Applied Regression Analysis: Homework 5” (PDF)

Instructions: Click on the link above, which will take you to the website of BUS 41100. Scroll down to Homework 5 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 3 hours.

2.2 Multiple Correlation and R2   - Reading: University of Florida: Alan Agresti’s Statistical Methods for the Social Sciences II: “Chapter 11: Multiple Regression and Correlation” 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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2.3 Inference for Multiple Regression and Coefficients   - Reading: University of Florida: Alan Agresti’s Statistical Methods for the Social Sciences II: “Chapter 11: Multiple Regression and Correlation” 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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2.4 Relationships between Predictors   - Reading: Jeff Miller and Patricia Haden’s Statistical Analysis with the General Linear Model: “Chapter 16: Relationships among Predictors” Link: Jeff Miller and Patricia Haden’s Statistical Analysis with the General Linear Model: “Chapter 16: Relationships among Predictors” (PDF)

`````` Instructions: Click on “Download the book as a PDF file” to save
course. Read “Chapter 16: Relationships among Predictors.” This
chapter will address an important aspect of regression analysis,
that is, the relationships between the different predictor
variables. You will learn about the “context effect,” which is a
situation when the usefulness of a predictor depends on which other
predictor variables are included in the model. You will also learn
about the use of the Venn diagram to visualize the relationships
between predictors that lead to redundancy, error reduction, and
suppressor effects.

Studying this chapter should take approximately 4 hours.

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• Reading: University of Florida: Alan Agresti’s Statistical Methods for the Social Sciences II: “Chapter 11: Multiple Regression and Correlation 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

2.5 Partial Correlation   - Reading: University of Florida: Alan Agresti’s Statistical Methods for the Social Sciences II: “Chapter 11: Multiple Regression and Correlation” 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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• Assessment: McGraw Hill: Bowerman, O’Connell, Schermer, and Adcock’s “Business Statistics in Practice: Multiple Choice Quiz for Chapter 12” Link: McGraw Hill: Bowerman, O’Connell, Schermer, and Adcock’s “Business Statistics in Practice: Multiple Choice Quiz for Chapter 12” (HTML)

Instructions: Select your answer from choices given for each question and click on “Submit Answers” at the bottom of the webpage when you have answered all the questions. The webpage will tell you whether your answer is correct and what the correct answer is.

Completing this quiz should take approximately 1 hour.