SPATIAL DATA ANALYSIS AND MAPPING:Regression and Spatial Regression

University of Toronto at Mississauga | Department of Geography | Winter 2016 SPATIAL DATA ANALYSIS AND MAPPING (GGR276) Assignment 2: Regression and Spatial Regression Objectives: 1. Develop skills related to the application of statistics to the analysis of hypotheses. 2. Develop familiarity with simple linear regression and spatial autocorrelation using ArcGIS. 3. Understand how to implement and interpret geographic weighted regression using ArcGIS. 4. Understand how to implement and summarize results of a statistical experiment in a written report. DUE DATE: Sunday June 5, 2016 @ 11:59PM Instructions: This lab is worth a total of 48 marks, and 15% of your final course grade. You are to work alone and finish the questions in Blackboard. Introduction A simple linear model such as Y = ax + b is also known as a global model – the relationship between y and x is assumed to be constant across the study area. The residuals from the global model are assumed to be independent and normally distributed. However, this is not always the case with data for spatial units. Spatial heterogeneity exists when the structure of the process being modelled varies across the study area. Geographically weighted regression (GWR) is a method of analyzing spatially varying relationships. This assignment will determine how residents with university degrees affect the proportion of residents with income in the dissemination areas (DA) of Mississauga. First you will determine if there are any spatial patterns (e.g., autocorrelation) that exist in each variable. Then, you will perform a simple linear regression and GWR to determine which regression method is more suitable for the dataset. Finally, you will have to determine how much variation in the proportion of residents with income can be explained by their education level (i.e., university degree) in Mississauga. 2 PART 1: Data and Data Presentation In this section, you will explore select statistical information from the 2001 Canadian Census using ArcMap. Here, you will learn how to create a graphical representation of the statistical data. STEP 1: Assignment 2 data (files listed below) are located in your StudentWork folder, \medusa StudentWorkYourUTORIDGGR276_2016LabLab2 Assign2_data.dbf Assign2_data.shp Assign2_data.prj Assign2_data.shp.xml Assign2_data.sbn Assign2_data.shx Assign2_data.sbx The shapefile (Assign2_data.shp) will be used for this assignment; the full description of the data contained in the file can be found in Table 1. Data was extracted from the 2001 Canadian Census and represents total population by school attendance – 20% Sample Data in each DA for the City of Mississauga. Table 1. Column Descriptions Column Description FID Unique identifier for each dissemination area DA_LAND_ID Unique identifier for each polygon (or subdivisions) UNIVERSITY Number of residents with university degree WITH_INCOM Number of residents with income FieldID Unique identifier for each row STEP 2: Start ArcMap from windows Start > Programs > ArcGIS >ArcMap 10.1 Start a new empty map in ArcMap. 3 STEP 3: Add Assign2_data.shp to ArcMap using function. Be sure to connect to the medusa folder in order to access your work by selecting the Connect to Folder icon. From here, you will be presented with a window; type in \medusaStudentWork(Your UTORid) as the path directory: STEP 4: Check data attributes.  Under Layers, right click Assign2_data and click ‘Open Attribute Table’ in the popup menu.  In the attribute table, you will see two variables: UNIVERSITY (residents with a university degree) and WITH_INCOM (residents with income). Please close the attribute table afterwards. 4 STEP 5: Classify each variable (UNIVERSITY and WITH_INCOM) to 6 classes and export the classification maps.  Right click Assign2_data and click ‘Properties’ in the popup menu. Go to ‘Symbology’, then click ‘Quantities – Graduated Colors’, select ‘University’ in the value field, Give ‘6’ in the classes menu, then click ‘OK’  In ArcMap – View, change ‘Data View’ to ‘Layout View’. 5  In ArcMap – Navigate the main menu and find Insert. Using the options on the drop down menu, insert the necessary map elements (Title, North Arrow, Legend, Scale Bar, etc.) Data View Layout View 6  Open the attribute table again, sort the ‘University’ field by right clicking ‘University’ in the attribute table, and select ‘Sort Descending’ in the popup menu, and select 3 rows in the attribute table with the largest UNIVERSITY values. This will appear on the map layout as highlighted DAs. 7  In ArcMap – File, click Export Map to export the map you made to JPEG format (with the three highlighted polygons displayed in map)  Under Layers, right click Assign2_data and go to Selection in the popup menu, and then click Clear Selected Features.  Repeat a) – f), but instead use the ‘WITH_INCOM’ variable in the field when conducting a). 8 Basic Guidelines for Making a Map Data in maps:  The data (map) should take up the majority of the area (avoid excessive white space) Titles:  Should not be sentences, but simple, to the point, and easy to read while adequately describing the map being shown. Scale bars:  Should be an appropriate size/length (i.e., should never extend all the way across a page).  Should use appropriate measurement units (e.g., kilometres for Mississauga, metres for UTM campus).  Should use the metric system which is more compatible with the rest of the world. Borders:  Maps should have a border or “neatlines”; usually in black. North Arrows:  North arrow should be visible, but not distracting. Should not cover any part of the map. Legends:  Legends should be clear as to what they are describing.  Legends do not need a heading ‘Legend’ or ‘Key’. Text on Map:  Text should NEVER cross other text or other features of the SAME color.  Text should be readable! Name on Map:  Unless the map is being published, names are generally kept outside of the map. Your name can go underneath the neatline on the bottom right side. Data Source:  The source of the map data is a necessity to give credit to whomever provided the data (e.g., government agencies). It should be provided underneath the neatline on the bottom right side. Datum and Projection:  The datum and projection of the map should always be provided so that your reader may identify what properties of the map are preserved or distorted. For instance, different datum and projections will preserve certain properties correctly while distorting others (e.g., size, shape, area, and angle). It should be provided underneath the neatline on the bottom right side. 9 Part I Questions: 1. This study will determine whether residents with university degrees (UNIVERSITY) affect the proportion of residents with income (WITH_INCOM) in Mississauga. Determine which variable in the dataset is the dependent and independent variable. What is the relationship between the dependent and independent variable? Submit your answer to Blackboard. (2 marks) 2. Using the graph below, try to understand the relationship of the linear regression model between the variables UNIVERSITY and WITH_INCOM. (4 marks) 3. Upload the two maps you produced in PART 1: STEP 5 (Please pay attention to basic guideline and try to make your map look professional. You will need a legend showing your colour ramp, but you do not need to include symbology for the blue outlined polygons). Upload a single JPEG screenshot (with readable text) with both maps to Blackboard. (10 marks) 4. Review covariance and select the most correct answer on Blackboard. (2 marks) 5. Describe the two maps you produced. Does university degree or income co-vary in certain area(s)? (4 marks) 10 PART 2: Measuring Spatial Autocorrelation In this section, you will learn how to perform spatial autocorrelation in ArcMap and determine if spatial autocorrelation exists for each variable. STEP 1: Go to: ArcMap > ArcToolBox > Spatial Statistics Tools > Analyzing Patterns > Spatial Autocorrelation STEP 2: In the Spatial Autocorrelation panel, use ‘Assign2_data’ as the Input Feature Class, ‘UNIVERSITY’ as Input Field, check ‘Generate Report’ and click OK. 11 STEP 3: The window below will pop-up at the lower-right corner of screen. Click to open the spatial autocorrelation result. STEP 4: Spatial Autocorrelation results will open as shown below. Copy the results for later use. STEP 5: in the messages, find the location of the MoransI_Result.html file > Open it to check the results. STEP 6: Repeat STEP 2, but instead use the ‘WITH_INCOM’ variable in the input field. 12 Part 2 Questions: 6. Spatial autocorrelation analysis is important when dealing with spatial data. Go to Blackboard and select all of the statements that are true of spatial autocorrelation. (2 marks) 7. Report the autocorrelation outputs for the variable UNIVERSITY. Upload a JPEG screenshot that includes the Spatial Autocorrelation Report, Global Moran’s I Summary, and Dataset Information. (1 mark) 8. Interpret the autocorrelation results (i.e., Moran’s Index and the p-value) and indicate whether spatial autocorrelation exists and explain your reasoning. (4 marks) PART 3: Simple Linear Regression In this section, you will learn how to perform simple linear regression and geographically weighted regression in ArcGIS and understand the difference between them. Again, we will use the same dataset containing the variable of residents with university degrees (UNIVERSITY) and the variable of residents with income (WITH_INCOM) in Mississauga. STEP 1: Simple Linear Regression In ArcMap > ArcToolBox > Spatial Statistics Tools > Modeling Spatial Relationships > Ordinary Least Squares 13 STEP 2: In Ordinary Least Squares panel, use ‘Assign2_data’ as Input Feature Class, ‘FieldID’ as Unique ID Field, save your work via Output Feature Class using an appropriate file name, and determine ‘Dependent Variable’ and ‘Explanatory Variables’. Please note: an explanatory variable is also called an independent variable. Click “OK” STEP 3: Open the results of Ordinary Least Squares, please record the results for future use. Part 3 Questions: 9. Report the OLS regression output. Upload a JPEG screenshot with the OLS output from ArcMap (OLS Diagnostics). (1 mark) 10. Using the OLS output, interpret the results of the multiple R 2 , Adjusted R2 and Akaike’s Information Criterion (AIC). Provide a clear statement summarizing your conclusions based on this regression analysis. (8 marks) 14 PART 4: Geographically Weighted Regression STEP 1: Geographically Weighted Regression In ArcMap > ArcToolBox > Spatial Statistics Tools > Modeling Spatial Relationships > Geographically Weighted Regression STEP 2: In Geographically Weighted Regression panel, use ‘Assign2_data’ as Input features, determine ‘Dependent variable’ and ‘Explanatory variable(s)’, save your work via Output feature class using an appropriate file name and then click ‘OK’. STEP 3: Open the results of Geographically Weighted Regression. Before closing the dialogue, please record the results from the Geographically Weighted Regression. 15 Part 4 Questions: 11. Upload a JPEG screenshot with the GWR output from ArcMap. (1 mark) 12. What is the conceptual difference between GWR and OLS? Compare the GWR results with the OLS results and indicate which regression is more suitable for this study. (5 marks) 13. While the OLS or simple linear regression method is a very powerful and commonly used analysis, there are also several disadvantages to using this method. Go to Blackboard and select the statements that are true of OLS. (2 marks) 14. GWR is a commonly used regression method for spatial data. Select the statements that are true of GWR. (2 marks) Reminder: please answer all questions electronically using Blackboard. The End

 

 

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