Quantifying Relationships with Regression Models

While graphs are useful for visualizing relationships, they don't provide precise measures of the relationships between variables. Suppose you want to determine how an outcome of interest is expected to change if we change a related variable. We need more than just a scatter plot to answer this question. What should you do, for example, if you want to calculate whether air quality changes when vehicle emissions decline? Or if you want to calculate how consumer purchasing behavior changes if a new tax policy is implemented? To calculate these predicted effects, we can use a regression model. This module will first introduce correlation as an initial means of measuring the relationship between two variables. The module will then discuss prediction error as a framework for evaluating the accuracy of estimates. Finally, the module will introduce the linear regression model, which is a powerful tool we can use to develop precise measures of how variables are related to each other.

Now that you've got a handle on the basics of regression analysis, the next step is to consider how to evaluate and modify a basic regression model. This module will introduce you to a common measure of model fit and the three core assumptions of regression analysis. In addition, we'll explore the special circumstance of conducting a regression analysis with a binary (AKA dummy) treatment variable. Dummy variables, which take on two values, are frequently used in statistics. Understanding how to use and interpret dummy variables provides a foundation for developing a multivariate regression model, which we'll get to in the next module.

The bivariate regression model is an essential building block of statistics, but it is usually insufficient in practice as a useful model for descriptive, causal or predictive inference. This is because there are usually multiple variables that impact a particular dynamic. Whether you are modeling political behavior, environmental processes or drug treatment outcomes, it is almost always necessary to account for multiple influences on an outcome of interest. This module will introduce the multivariate model of regression analysis and explain the appropriate ways to interpret and evaluate the results from a multivariate analysis.