In the previous module, we learned methods we could use to decide whether to reject a null hypothesis based on the evidence we have. However, what if we want more than a simple yes/no answer and wish to precisely predict how the outcome changes as the predictors change? This is the reason we use regression models, as we will learn in this module. This module has four lessons, and the division is based on the nature of the outcome variable: if it is a continuous variable, we use simple or multiple linear regression; if it is a binary categorical variable, we use logistic regression. These represent some very common and basic statistical models; there are many more regression methods in the field, but learning the basic concepts well will help you quickly pick up other methods when you need to. You will notice that some concepts cross over from epidemiology, such as risk, odds, confounding, bias, etc. It is helpful to possess some prior knowledge in epidemiology, but if you don’t, these concepts will also be explained in this module.

Resources on regression can vary a great deal in their depth and complexity. Don’t let the math scare you. Focus on the main ideas to start, and add the mathematical details as you continue progressing in the topic.

The learning activity in this module asks you to go through some regression models. Even more so than hypothesis testing, the tedious calculation parts are done by the computer, but you will need to answer questions about the model and about using the model. These are essential skills that you will need in order to understand research literature and reports.

Upon completion of this module, students should be able to:

• Understand linear relationships, outliers, and the basics of correlation
• Understand the difference between correlation and simple linear regression, and when to apply one or the other
• Understand homoscedasticity and its applications to correlation and regression
• Understand linear regression and how it relates to prediction
• Understand multiple linear regression and its applications
• Understand simple logistic regression analysis
• Understand multiple logistic regression analysis and distinguish between adjusted and unadjusted regression coefficients
• Be able (1) to distinguish between risks, e.g., absolute and relative risks, as well as odds and odds ratios, and (2) to differentiate relative risks from odds ratios and know how to conduct both methods
• Be able (1) to distinguish between correlation, linear and multiple regression, and logistic regression, and (2) to understand the purpose and methods of linear (simple and multiple) and logistic regression, including when to use each of them
• Be able to specify regression models and interpret regression results

Module 5: Lesson 1: Simple Linear Regression Analysis

Student Learning Objectives:

Upon completion of this lesson, you will be able to:

• Understand linear relationships, outliers, and the basics of correlation.
• Understand the difference between correlation and simple linear regression, and when to apply one or the other.
• Understand homoscedasticity and its applications to correlation and regression.
• Understand linear regression and how it relates to prediction.

Approximate time required to complete the readings (at 144 words/minute) and assignments for this module: 5 hours.

Required Learning Resources and Activities

Module 5: Lesson 2:  Multiple Linear Regression Analysis

Student Learning Objectives:

Upon completion of this lesson, you will be able to:

• Understand multiple linear regression and its applications.

Approximate time required to complete the readings (at 144 words/minute) and assignments for this module: 1 hour.

Required Learning Resources and Activities

Module 5: Lesson 3:  Logistic Regression Analysis

Student Learning Objectives:

Upon completion of this lesson, you will be able to:

• Understand simple logistic regression analysis.
• Understand multiple logistic regression analysis and distinguish between adjusted and unadjusted regression coefficients.
• Be able (1) to distinguish between risks, e.g., absolute and relative risks, as well as odds and odds ratios, and (2) to differentiate relative risks from odds ratios and know how to conduct both methods.

Approximate time required to complete the readings (at 144 words/minute) and assignments for this module: 4 hours.

Required Learning Resources and Activities

Module 5: Lesson 4: Overview of Correlation and Regression Analysis

Student Learning Objectives:

Upon completion of this lesson, you will be able to:

• Be able (1) to distinguish between correlation, linear and multiple regression, and logistic regression, and (2) to understand the purpose and methods of linear (simple and multiple) and logistic regression, including when to use each of them.
• Be able to specify regression models and interpret regression results.

Approximate time required to complete the readings (at 144 words/minute) and assignments for this module: 1 hour.

Required Learning Resources and Activities