Regression Analysis

Part 1

     With this regression equation the news station was correct in saying that there is a positive correlation between crime rates and free lunches. Although there is a significant positive correlation, between the two variables, there are probably more important variables that influence crime rate than free lunches given out in schools.  The equation to find out the percentage of free lunches given out is as follows Y=21.819+1.685(X). If there is a crime rate of 79.7, the percentage of persons that will receive a free lunch will be 2.16%. 

Part 2

Introduction:

     This assignment gave the student experiencing running regression analysis using a real life situation. This particular example relates to the University of Wisconsin school system. The system wants to know what factors influence a student's decision to attend a particular university. Since the options for attending a particular school are nearly endless, three factors have been chosen for the student to use. The student will run regression analysis on the University of Wisconsin Eau Claire and the choosing of one other school, in this case, the University of Wisconsin La Crosse. 

Methods:

     The data used in this lab was provided by the professor. The three variables used in this analysis were median household income, percent of people with a bachelors degree and population distance. The third variable, population distance, was created by normalizing two fields within the data set. total population of each county was divided by distance from the university. The main reason this was done was to reduce the influence of large population centers from skewing the regression analysis. 

     The first data sets were in excel files. The first step was to take the data needed from the original file and copy it into a new excel spreadsheet. Once this sheet was created, it was then brought into SPSS to run regression analysis. Once the regression analysis was completed on all variables for both schools, significant variables then needed to be identified. There were two significant variable for Eau Claire and three significant variables for La Crosse. Once these variables were identified, regression was ran on them again. This second time, the residuals were then saved in the same SPSS worksheet. The saved residuals allow for a spatial component to be connected to the raw numbers. The numbers allow to viewer to see what is significant, but the spatial connection allows to viewer to see what areas are most significant. 

     Once all the residuals were collected for each variable, the table was then exported as a dBase table. Once the table was exported, it was then brought into ArcMap. After being brought into ArcMap, it was then joined with a shapefile of all the counties in the state of Wisconsin. This join allows for a spatial representation of all the residuals.

Results:

     The results of this lab were very interesting. The table below (Table 1) shows the results of the regression analysis with the variable population distance. The table shows that this variable is significant. Although you can see it is significant, it is hard to see where the most students are coming from. 

Table 1 Shows the population distance regression analysis
 for students attending the University of Wisconsin Eau Claire.

The figure below (Figure 1) shows where most students are coming from to attend Eau Claire. 

Figure 1 show the residual of population distance for
students attending the University of Wisconsin Eau Claire. 

As the map shows, many of the students attending the University of Wisconsin Eau Claire come from counties that typically have higher populations. Areas that are red or yellow in color show a higher amount of students than expected, while light blue and dark blue show which areas are sending less students to the university. 

The second variable that was significant involving Eau Claire was the percentage of people with a bachelors degree. 

Table 2 Shows the percent of people with a Bachelors degree
regression analysis for students attending the University of Wisconsin Eau Claire.

Figure 2 showsthe residual of percent of people with a bachelors degreefor students attending the University of Wisconsin Eau Claire.

The table show above (Table 2) shows the significance of the percentage of people with a bachelors degree and the enrollment of students at Eau Claire. The numbers show that there is a very steep slope and this is a significant factor, but it is hard to determine much more than that. The figure to the left (Figure 2) shows where most students are coming from. As the map shows, areas in red or gold have a high percentage of people with a bachelors degree and higher amounts of students are attending the university from those areas. It does not appear to have a tie with population. 

The next three tables shown below (Table 3, Table 4 and Table 5) show the results of the significant variables for the University of Wisconsin La Crosse. 

Table 3 Shows the population distance regression analysis for students attending the University of Wisconsin La Crosse.

Table 4 Shows the percent of people with a Bachelors degree
regression analysis for students attending the University of Wisconsin La Crosse.

Table 5 Shows the median household income regression analysis for students attending the University of Wisconsin La Crosse.

As the three tables show above, all the variables were extremely significant in the regression analysis. The figures shown below (Figure 3, Figure 4 and Figure 5) show the spatial context of these different variables. 

Figure 3 shows the residual of median householdincome for students attending the
 University of Wisconsin La Crosse.

Figure 4 shows the residual of percent of
people with a bachelors degree for students
  attending the
 University of Wisconsin La Crosse.

The map to the above (Figure 3) shows the median household income. As this map shows, median household income by county only seems to have a great effect on La Crosse county, with slight effects happening in Dane, Milwaukee and Waukesha county. The map above (Figure 4) show the percent of people with bachelors degrees and the effect it has on enrollment. Once again it seems to only have a great effect on La Crosse county, and a slight positive effect in counties that have higher populations. The third map shown below (Figure 5) show the results of the variable population distance. As the map shows, more students come from Dane and Waukesha counties than what would be expected. Most of the northern part of the state is well below the average of what the expected mean enrollment would be. 

Figure 5 shows the residual of population
distance for students attending the
 University of Wisconsin La Crosse.

Conclusions:

This lab teaches the student how useful regression analysis can be. The numbers themselves are useful, but incorporating the spatial component allows for the viewer to have a better understanding of the data. Mapping the data allows for trends to be easily noticed and not passed over by looking at the raw numbers of the regression.