# GEOG 683 Introduction to Geographic Analysis Lab 9 Regression

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```					                GEOG 683: Introduction to Geographic Analysis
Lab 9: Regression

Assigned on Nov. 28, 2005 (Monday, 10th week)
Due at the beginning of the final December 6th, 2005 (preferably Dec. 2nd, Friday)
T.A.: Fang Ren (ren.21@osu.edu 1083 Derby Hall, 688-3936)

1. Overview of Lab 9
The goal of this lab is for students to effectively implement bivariate regression in the
SPSS and GeoDa environment.
2. Setting up Lab 9

•   Copy all the files from X:\fren\G683\lab9 to your folder.
•   If your BEADATA file from the previous labs has HIGSCHL9, POVFAM9, and
BEADATA.xls into SPSS and save it as lab9_data.sav.
•   Open lab9_data.sav in SPSS.

3. Statistical Relationships:
(Read Ch. 13 and 14 of McGrew and Monroe)

(1) Bivariate Regression Analysis

•   We are interested in the relationship between education (HIGSCHL9) as an
independent variable and poverty level (POVFAM9) as a dependent variable (note
that HIGSCHL9 is defined as % of people with a high school diploma and higher).
In other words, we are trying to find how well HIGSCHL9 can be used to predict
POVFAM9.

•   Creating a Linear Fit Plot
o Choose Graphs ? Scatter/Dot ? Simple Scatter? Define and put
HIGSCHL9 in the x-axis box and POVFAM9 in the y-axis box.
o Activate the Chart Editor and click points in the graph to select them (all the
points should be blue at this moment). Click Add Fit Line button in the toolbar
and choose to add a linear fit line in the popup dialogue.
o Title and label your graph appropriately.

•   Conducting a Bivariate Regression
o Select Analyze ? Regression ? Linear
o Choose POVFAM9 in the Dependent and HIGSCHL9 in the Independent
variable.
o In the Statistics panel, check Estimates, Model Fit, R-squared change, and
descriptives.
o Under the Save panel, check unstandardized and standardized under residuals.

1
Assignment I
1. Hand in the linear fit scatterplot.
2. Report the results of your bivariate regression analysis in a table format that should
include regression coefficients (values, standard errors, t-values, and p- values),
coefficient of determination, and F-value and its p-value.
3. Interpret the t-value for HIGSCHL9 and its p- value.
4. Interpret the coefficient of determination.
5. Interpret the F-value and its p-value.
6. Write the equation for the regression line you just found. What is its slope?
7. Interpret the regression coefficients (for intercept and HIGSCHL9) in a substantive
way. Is there a relationship between HIGSCHL9 and POVFAM9? If there is, what
is the direction of the relationship?
8. Discuss what a residual is and how we may use it for spatial analysis.
9. Using your regression equation, predict the value for POVFAM9 when
HIGSCHL9 = 20%.

(2) Multiple Regression Analysis

Assignment II
1. Report the results of your multiple regression analysis in a table format that should
include regression coefficients (values, standard errors, t-values, and p- values),
coefficient of determination, and F-value and its p-value.
2. Interpret the regression coefficient for FEHEAD9 in a substantive way. In other
words, what does it mean?
3. How does the fit of this model compare with the model without FEHEAD9?
Discuss t- values, F- values, and p-values.
4. Make and submit a scatter plot for each independent variable and the standardized
residuals to evaluate the residuals. Do the plots suggest any non-constant variance
problems in the data?
5. Should FEHEAD9 stay in the regression model? Why or why not?

(3) Brushing Scatterplot and Linking Scatterplot and Map

In this exercise, we will practice how to use brus hing and linking functions in GeoDa to
assist our regression analysis.

•   Double-clicking on its icon GeoDa0951 on the desktop. In the File Menu, select
Open Project, or click on the Open Project toolbar button.
•   Select the BEADATA (beadata.shp) as the Input Map in the file dialog that
appeared, and leave the Key variable to its default BEAFIPS. Finally, click on OK
to launch the map
•   Click on      to open the attribute table associated with the map.
2
•   Invoke the scatter plot functionality from the menu, as Explore ? Scatter Plot, or
by clicking on the Scatter Plot toolbar icon      . This brings up the Variables
Selection dialog
•   Select POVFAM9 in the left column as the y variable and in the right column as
the x variable. Click on OK.
•   Resize three windows and place the map and the scatterplot above the table, so that
you are able to view three windows at the same time.
•   The blue line through the scatter is the least squares regression fit. Is the slope
same as the regression parameter you got from SPSS?
•   Right click on the scatterplot and click on Exclude Selected
•   Create a small selection rectangle on the scatterplot and hold down the Control
key. Once the rectangle starts to blink, the brush is activated.
•   From now on, as you move the brush (rectangle), the selection cha nges: some
points return to their original color and some new ones turn yellow. As this process
continues, the regression line is recalculated on the fly, reflecting the slope for the
data set without the current selection.
•   The full power of brushing becomes apparent when combined with the linking
functionality, which means that the selection from the scatter plot will be reflected
in the map. In our case, the selected economic area will be highlighted. (Figure 1)

Figure 1: Brushing and Linking functions

•   Not only the selection is reflected in the map, but also reflected in the attribute
table. If you want to get more information on the selected areas, you can stop the
brushing function by a left click on the scatterplot. Activate the table window, and
select Table ? Promotion to drag the selected records to the top of the table.
•   Activate the map window, and select any economic areas in the map by holding
left key and drawing a circle. What happens in the scatterplot and the slope?

3
Assignment III

1. Eliminate five (or more) areas from south region, and hand in the corresponding
map and the scatterplot as Figure 1. Explain the effect of these removed areas on
the regression lines.
2. Briefly discuss an application in which you might utilize the brushing and linking
functio ns to facilitate your analysis.

4. Log Out and Wrap Up
o Do not forget to log out.
o Your hand-in should look like a professional report which has a cover sheet with
your name, lab title, date, section number, and where documents, tables, and
graphs are presented in order.
o Feel free to make comments or suggestions about the Geography 683 lab sessions and
your overall experience in this portion of the class at the end of your assignment.

4

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