Lesson 5 Overview

Regression analysis is a statistical method used to estimate or predict the relationship between one or more predictor variables (also called independent variables). The independent variables are selected with the assumption that they will contribute to explaining the response variable (also called the dependent variable). In regression, there is only one dependent variable that is assumed to “depend” on one or more independent variables. Regression analysis allows the researcher to statistically test to see how well the independent variables statistically predict the dependent variable. In this week’s lesson, we will provide a broad overview of regression, its utility to predict something, and a statistical assessment of that prediction.

Scatterplot with trendline of murder rate by drug arrest rate

Figure 5.0: A scatterplot and regression equation showing how murder rate (dependent variable) and drug arrest rate (independent variable) are related for selected U.S. cities

Credit: Kessler, © Penn State University, licensed under CC BY-NC-SA 4.0 [1]

Learning Outcomes

At the successful completion of Lesson 5, you should be able to:

perform descriptive statistics on data to determine if your variables meet the assumptions of regression;
test these factors for normality;
understand how correlation analysis can help you to understand relationships between variables;
create scatterplots to view relationships between variables;
run a regression analysis to generate an overall model of prediction;
interpret the output from a regression analysis; and
test the regression model for assumptions.

Checklist

Lesson 5 is one week in length. (See the Calendar in Canvas for specific due dates.) The following items must be completed by the end of the week. You may find it useful to print this page out first so that you can follow along with the directions.

Lesson Roadmap
Step	Activity	Access/Directions
1	Work through Lesson 5	You are in Lesson 5 online content now.
2	Reading Assignment	Read the following section of the course text: Chapter 5, "Spatial Relations", pages 101-106. Also read the following articles, which registered students can access via the Canvas module: Beale, C. Lennon, J., Yearsley, J., Brewer, M., and Elston, D. (2010). Regression analysis of spatial data [2]. In Ecology Letters, 13: 246-264. Esri: Regression analysis basics [3]. Rosenshein, L., Scott, L. and Pratt, M. (2011) Finding a meaningful model. [4] ArcUser Winter: 40-45. Watch the following video about modeling spatial relationships using regression analysis [5]. You need only watch until minute 33. Though, if you're keen to learn more about geographically weighted regression, you can watch the remainder of the video.
3	Weekly Assignment	This week’s project explores conducting correlation and regression analysis in RStudio. Note that there is no formal submission for this week’s assignment.
4	Term Project	Interactive peer review: Meet with your group to receive and provide feedback on project proposals.
5	Lesson 5 Deliverables	Lesson 5 is one week in length. (See the Calendar in Canvas for specific due dates.) The following items must be completed by the end of the week. Complete the Lesson 5 self-test quiz satisfactorily (you have an unlimited number of attempts and must score 90% or more). Contribute to the 'Reflection on the Regression Reading' discussion forum. The paper you will discuss is available in the discussion forum. Term Project: Meet with your group for the interactive peer review and post to the 'Term Project: Peer-Review' discussion forum in Canvas.

Questions?

Please use the 'Discussion - Lesson 5' discussion forum to ask for clarification on any of these concepts and ideas. Hopefully, some of your classmates will be able to help with answering your questions, and I will also provide further commentary where appropriate.