Regression Analysis

Part I:

The regression of crime rate to percentage of students getting free lunch has a significant level of .005, indicating that it is indeed significant. 48.5% of the students will get free lunches when the crime rate is 79.7 per 100,000 people. I'm confident that there is a relationship, I just don't think that relationship is quite as strong as the local news station might be implying. 

Part 1 

Part II:

Introduction:

The UW system wants to know why students choose the schools they're going to. In order to analyze this, spatial regression analysis is to be performed on data regarding University enrollment and County population.

Methods:

Testing spatial regression was done through three separate equations for two schools, Eau Claire and Milwaukee. The null hypothesis states that there is no relationship between the two variables. The alternate hypothesis states that there is a relationship between the two variables. The variables we tested against the number of students attending each school were: population divided by distance, percentage of the county population with a bachelor’s degree, and median household income per county.

Results:

Figure 1

Figure 2

For both schools, only two tests from each were deemed significant, population divided by distance and percentage of the county population with a bachelor’s degree. Because the significance level of each of these tests was .005 or smaller, for each of these we REJECT THE NULL! The Eau Claire population divided by distance to student regression (Figure 1) has a significance level of .000 and has an r² of .945, showing this regression to be strong. The Eau Claire Bachelor Degree to student regression (Figure 2) has a significance level of .003 and has an r² of .121, showing this regression to be very weak. The Milwaukee population divided by distance to student regression (Figure 3) has a significance level of .000 and has an r² of .922, showing this regression to be strongly correlated. The Milwaukee Bachelor Degree to student regression (Figure 4) has a significance level of .001 and has an r² of .160, showing this regression to be weakly correlated.

The Significance values for the number of students attending to Median Household Income had significance values of .104 and .027 for Eau Claire (Figure 5) and Milwaukee (Figure 6), respectively. Because both of these significance levels are greater than .005, both FAIL TO REJECT THE NULL! 

Figure 3

Figure 4

Figure 5

Figure 6

When looking at Residual Map 1, it can be seen that areas with larger populations (other than Milwaukee) have higher numbers of students attending Eau Claire than the regression would predict, however, most of the state closely follows the predicted regression. When looking at Residual Map 2, it seems that closer counties deviate higher than counties further away. Regardless of what the symbology of Residual Map 3 seems to indicate, the map shows that areas with higher populations (other than Milwaukee) deviate higher from the regression than those with lower populations that are closer. Residual Map 4 shows small rural counties with smaller populations and counties closer to Milwaukee as deviating higher than the regression. For all of the maps, distance is the most common influence on school selection throughout the state. Percentage of the population with a bachelor’s degree has some influence, but would perhaps be more indicative if it were weighted by distance as well.

Residual Map 1

Residual Map 2

Residual Map 3

Residual Map 4