Introduction

In all fields of science, we are often concerned with determining whether the values of one variable we can measure (the independent or explanatory variable) can be used as a predictor of another quantitative value (the dependent variable). A simple example would be the relationship between height and weight in human beings. In any randomly chosen sample, the weight of the people in the group tends to be positively correlated with their height. Put another way, as the measured height of people in the group goes up their weight tends to also be higher. Using linear regression analysis allows us to determine the best-fit line through the height vs. weight data, and we can then use that line to predict the weight of people for any given height. Oftentimes there are multiple independent variables which together best explain the variability in a dependent variable, and for that we use multiple linear regression to find the model that numerically describes that relationship. A good example might be trying to predict human blood pressure measurements based on height, weight, daily salt intake and number of steps walked per day.

Many of the problems we face in environmental analyses have a spatial component, which complicates the use of linear regression techniques. For instance, we might be interested in whether the amount of lead (Pb) in the blood of elementary school students is correlated with household median income in a group of counties. We could use simple least-squares linear regression on the data, but the distribution of the resident children geographically may also affect the relationship. In the Module #09 - Linear Regression with Spatial Data Module you will learn how to use tools in ArcGIS Pro for finding statistically significant correlations in the variables within spatial datasets, while addressing the issues of spatial autocorrelation.

Reading Assignments

Follow the links to read each of the articles below prior to taking the Quiz for this week. If you see a popup from an Elsevier article like this one, click on the link that says "Continue Without Registering" to connect to the article. Links to journal articles will sometimes require you to sign in to the UCF Library with your NID and password before taking you to the online database where you can download the article. If you have trouble downloading an article using the link provided, click on UCF Library Tools at left, follow the link for Databases List, then search for the paper using the title and author information provided in the citation. You can also sign in to the OpenAthens Access page which will provide you full access to most journal articles. Contact the staff at the UCF Library for help if you cannot access an article.

Bennett, L., & Vale, F. (2023). Spatial statistics illustrated. Esri Press. ISBN-13: 978-1589485709 - Read the following sections from the required textbook:
- Chapter 1, Why spatial is special (pp. 8 - 18)
- Chapter 2, Means and Medians (pp. 19 - 45)
- Chapter 6, Modeling spatial relationships and making predictions (pp. 142 - 157)
Regression Analysis Basics- Read this ArcGIS Pro online help article that provides an introduction to linear regression for spatial data.
How OLS Regression Works - This ArcGIS Pro help article explains how to use and interpret the Ordinary Least Squares (OLS) regression model.
How Geographically Weighted Regression (GWR) Works - This ArcGIS Pro help article explains the tool for weighting the influence of input features to the linear regression based on their proximity to one another.
How Generalized Linear Regression Works - Read this ArcGIS Pro help article about how the GLR includes the OLS regression plus tools for Count (Poisson) and Binary (Logistic) regression.
Exploratory Regression (Spatial Statistics)- This ArcGIS Pro help article describes the tools for comparing the "goodness of fit" when you have multiple multivariate linear regression models for your data.
Interpreting Exploratory Regression Results- This ArcGIS Pro help article explains how to interpret the results from the Exploratory Regression tool.
Zhou, N., Hubacek, K., & Roberts, M. (2015). Analysis of spatial patterns of urban growth across South Asia using DMSP-OLS nighttime lights data. Applied Geography, 63, 292-303. - In this paper the authors correlated measurements of night-time lighting as measured by Defense Meteorological Support Program (DMSP) satellites to predict the Gross Domestic Product (GDP) of regions in South Asia including India, Pakistan and Afghanistan.
Zhang, H., Liu, Y., Chen, F., Mi, B., Zeng, L., & Pei, L. (2021). The effect of sociodemographic factors on COVID-19 incidence of 342 cities in China: a geographically weighted regression model analysis. BMC Infectious Diseases, 21(1), 1-8. - The authors used Geographically Weighted Regression (GWR) analysis to evaluate the relationship of COVID19 infection rates in China to several sociodemographic variables, including distance from Wuhan, the source of the infection.

ArcGIS Exercises and Lab Assignments

Follow the instructions in the Lab #09 - Linear Regression Tutorial assignment to access the "Introduction to Regression Analysis Using ArcGIS Pro" tutorial from the Esri Academy online training web site. After completing the online tutorial, you will upload the completion certificate to the Lab #09 assignment.

Discussion

There will be no Discussion assignment for Week #09.

Quiz

Take Quiz #07 - Linear Regression with Spatial Data after completing all other assignments for this week's module. The quiz may cover any of the material from the hands-on ArcGIS exercises or the reading assignments. The quiz is "open notes" so you can refer to any of the class materials to help you. However, keep in mind that the time limit on the quiz will not allow you to look up the answers to every question. Review what you've learned and be prepared before starting the quiz!