The Origin of UWEC Students: A Gravity Model Approach Ross Guida

The Origin of UWEC Students: A Gravity Model Approach Ross Guida Introduction At the University of Wisconsin-Eau Claire (UWEC), students come from all over the state of Wisconsin, but different factors influence the number of students that attend from the different areas of the state. More incoming freshmen come from counties closer in distance to Eau Claire than counties that are more distant. As Tobler s First Law states, Everything is related to everything else, but near things are more related to each other. The public university system in Wisconsin (UW schools) allows students to attend -year schools throughout various parts of the state. From UW-Superior in the northwest corner of the state to UW-Parkside in the southeast, UW-Green Bay in the northeast, and UW-Platteville in the southwest there are schools all over the state which are economical to get to by car and close to home for those who don t want to go too far away for college. A gravity model, where freshmen attending UWEC is equal to population divided by distance (S ECj = P j /D ECj ), approach can be used to analyze the location of where students attending Eau Claire come from. This model and the formula involved simply assist in showing the further away students are in the state, the less likely they will attend UWEC. Several other variables will be analyzed to assess their influence on UWEC s freshmen class. Variables by zip code for the state include median household income, total population population of college aged students, population of high school students, advanced degrees and all of these variables divided by distance from Eau Claire. Maps made in ArcMap GIS 9.3 and data calculations made in Microsoft Excel will be the primary sources of data used. The Existing Pattern and Conventional Reasons Standard Reasons for Attending College Students choose their undergraduate college based on many different things. For some, it s strictly about the most economical choice based on travel costs, in-state tuition, and other various cost based decisions. Others choose a school because they like the campus or the school has a specific major or program with a good reputation. Some even choose a school because their parents went there or they have family and friends who are or will be attending the school. The reason students attend college is because they want to and can afford to go on and obtain more knowledge beyond a high school education. A desire to learn more is what drives students to obtain a college degree, which is ultimately the goal at a -year university. The Pattern of UW-Eau Claire Origins UWEC students come from all over the state of Wisconsin. However, certain patterns are created when looking at the numbers of students from each area of the state. More students come from areas near Eau Claire than those further away (Figure 1). The simple Kriging map of the total number freshmen attending Eau Claire in the Fall of 2006 shows the highest number of students come from the counties closest to UWEC (Figure 1). This model does a good job in Guida 1

showing the closer students are more likely to attend UWEC than distant ones. Anomalies seem to appear around the areas of Green Bay, Ashland, LaCrosse, Stevens Point and Madison. These will be explained later in terms of their total population and why it can be expected to have higher populated areas sending more students to UWEC. UWEC Freshmen Distribution 2006 UWEC UW Campuses Freshman_Distribution_Kriging 1-1.81 1.81-2.3 2.3-3.11 3.11 -.. - 6.6 6.6-10.26 10.26-16.23 16.23-26.06 26.06-2.28 2.28-69 Figure 1 Income UWEC is a state school and as far as bargains go for college it s one of the best in the Midwest. Mapping the distribution of median household income for the state of Wisconsin can give some insight into where students originate (Figure 2). Since Eau Claire is looked at as an economical choice for college, it isn t expected the highest income areas would send the most students. Figure 2 shows this quite clearly when compared to Figure 1. High income areas are concentrated in the eastern third of Wisconsin with some of the peripheral income from the Twin Cities suburbs showing up directly west of Eau Claire. Students, however, do not come from the areas with highest income when comparing the two maps. In fact, median household income explains little of the student population at UWEC based on the comparisons. Guida 2

Median Household Income UWEC UW Campuses Med_HH_Income_Kriging 26,360-32,879.01 32,879.01-37,709.3 37,709.3-1,288.32 1,288.32-3,90.22 3,90.22-7,519.2 7,519.2-52,39.53 52,39.53-58,868.5 58,868.5-67,666.66 67,666.66-79,50.69 79,50.69-95,566 Figure 2 Education Students without a high school education don t attend college. To be a high school graduate or equivalent you need to have completed a certain number of years of school or obtained a satisfactory test score based on knowledge accumulated over the years. Generally, a student has turned 18 or will turn 18 within a year of graduation from high school. So, in order to better understand which part of the population is eligible to attend UWEC, we need to map the population in Wisconsin from the age of 15 (when students start high school) to the age of 25 (when students have either graduated college or have moved on to other opportunities). Figure 3 shows much of the high school and college aged population is concentrated in the southeast part of the state. Madison, Milwaukee, Racine, Kenosha, and Green Bay all have the largest populations so it s natural they have the highest population of those age 15 to 25. When looking at why some anomalies appear when looking at students attending UWEC (Figure 1), it becomes easier to explain when you look at the populations of high school and college aged students around LaCrosse, Green Bay, and Madison. Students from the southeast part of the state generally don t travel over three hours to attend UWEC since there are -year state schools closer. Intervening opportunities for the same programs are encountered when looking at the fact that nine schools are closer to the high population areas that UW-Eau Claire is (Figure 3). Guida 3

Students must ask themselves is it worth it to travel a greater distance to another state school with many similar opportunities. The general consensus seems to be the schools closer to the population centers of Wisconsin have enough opportunity to satisfy the need of those students. HIgh School Through College Age Population UWEC UW Campuses HS_thru_College_Age 82-323.77 323.77-92.8 92.8-73.25 73.25-1,080.71 1,080.71-1,577.19 1,577.19-2,288.6 2,288.6-3,308.17 3,308.17 -,769.17,769.17-6,862.8 6,862.8-9,863 Figure 3 Population/Distance Gravity Model A gravity model approach S ECj = P j /D ECj (where P j = Population of County j, andd ECj = distance from County j to UWEC) is commonly used when looking at the Spatial Organization Paradigm. In basic theory for this formula, the higher the population of a county and the closer to UWEC the county is, the more students are expected to be part of the freshmen class and UWEC. That also mean the further away a county is, all populations being the same, the less students we d expect to find. Also, the higher the population and the further away, there are also going to be less students among UWEC freshmen. Guida

General Figure shows the total population divided by the distance of each zip code from UWEC. So, the map shows all possible outcomes for the incoming freshmen class as given by the gravity model (Figure ). The map shows good spatial organization because the highest values are those closest to UW-Eau Claire. The largest number of students come from counties close to UWEC and they also have some of the highest numbers of incoming freshmen. The map also does a good job showing how certain highly populated areas like Milwaukee, Kenosha, Racine, Madison and Green Bay are expected to send more students that other less populated areas the same distance from UWEC (Figure ). When compared to the actual number of freshmen (Figure 1), the gravity model map showing the population over the distance (Figure ) some anomalies are present. Using the gravity model approach, more students are expected to come from areas in southeast Wisconsin when in fact the number is actually smaller. However, the areas directly around Eau Claire correlate well between the two maps. Total Population/Distance From Eau Claire UWEC UW Campuses Poverd_Kriging 1.65-2.22 2.22-33.78 33.78-56.35 56.35-109.66 109.66-235.58 235.58-533 533-1,235.8 1,235.8-2,89.66 2,89.66-6,813.51 6,813.51-16,069.5 Figure Guida 5

Statistical Analysis Looking at a scattergram of the incoming freshmen class with population over distance (P/D) on the x-axis and total number of UWEC freshmen on the y-axis (Figure 5) it becomes apparent the gravity model does a good job of estimating and describing where the incoming fresmen are expected to come from. The higher the P/D number, the greater the number of freshmen that can be expected from that zip code. For example, the point furthest to the right on the graph must represent an area close to UWEC. The population is relatively large and the distance is approaching 0. Therefore, the P/D will be high and the number of freshmen will be high. The cluster toward the bottom left part of the chart represents small numbers of freshmen for each zip code. That directly correlates with their P/D score because the further away from UWEC or the smaller the population of a place, the less incoming freshmen would be expected. Higher points between 30 and 0 freshmen and with a P/D number of less than 2,000 most likely represent nearby communities with relatively low populations but a large number of students who are attending UWEC due to its close proximity and economical costs. Using a coefficient of determination analysis with Microsoft Excel and the demographic data from ArcMap GIS 9.3, we can determine what percentage of each variable we can expect to describe the incoming freshmen class for UWEC (Table 1). The first column represents the variable and the second column is the coefficient of determination as given by percents. The Guida 6

first five variables represent variables with no distance factored in. The last five are the same variables divided by the distance from UWEC. Population decayed (population/distance) and advanced degrees decayed (advanced degrees/population) have the highest coefficient of determination percentages, indicating they are the best variables to use when trying to figure out where the freshmen from UWEC will come from. Looking at the decayed numbers, it is also apparent when looking at spatial organization, distance is the most important factor. Population, income, age of the population and those with advanced degrees are all simply information categories. They are concerned with space as content and not space at separation. Using the different variables helped effectively show spatial organization but dividing the variables by distance is what truly brought about results that are accurate. The population over distance number having the highest coefficient of determination also enforces the fact the gravity model approach is the most accurate approach taken out of the methods used. Other Measures of Attendance TABLE 1 Variable CD Population 20.7 Median HH Income 0.52 HS or Less 9.73 Hs or College 8.08 Advanced Degrees 9.98 Population Decayed 5.2 Median HH Income Decayed 3.63 HS or Less Decayed 50.2 Hs or College Decayed.13 Advanced Degrees Decayed 5.2 Competing UW Schools As discussed earlier, intervening opportunity will change the landscape when looking at spatial organization. UW schools have been placed at various places around the state and many of them have the same opportunities for college degrees. The ones mapped (Figures 1-7) show where in the state -year UW universities are located. While UW-Madison and UW-Milwaukee may be larger, they are also located in the largest metropolitan areas, making them different than the other UW schools. They also have extensive graduate school programs whereas most of the other universities are mainly for undergraduate coursework. So, as a result, more students close to the other UW schools will attend them instead of UWEC because there is no reason for most students to travel extra distance and spend more money with housing when the same or similar opportunities exist within closer proximity. College Aged Students/Distance Earlier, the number of high school and college aged students was specifically looked at when combined (Figure 3). But looking at the specific number of college aged students divided by the distance from Eau Claire can give a better understanding of the entire student base of UWEC instead of just the freshmen class (Figure 6). In fact, what it shows us is that from year to year, when comparing it to the total number of freshmen and the total population over distance Guida 7

maps, the student base doesn t seem to change much when looking at where UWEC students come from in the state of Wisconsin. College Aged Students/Distance from Eau Claire UWEC UW Campuses College_Aged_Students_Dist 0.086320303-1.6522179 1.6522179-2.315866 2.315866-3.88158813 3.88158813-7.58058351 7.58058351-16.3172886 16.3172886-36.9526257 36.9526257-85.691957 85.691957-200.8086 200.8086-72.7072 72.7072-1,11.90002 Figure 6 Advanced Degrees/Distance Looking at advanced degrees among the population of Wisconsin also helps to analyze where UWEC students may come from (Figure 7). Parents are likely to be the ones holding the advanced degrees and students with parents who are college educated are more likely to attend school themselves. It is just another measure to show where students are coming from and how the distance again affects this number. As describe earlier, advanced degree/distance has the highest coefficient of determination along with population over distance (Table 1). That means the advanced degrees/distance can explain 5.2% of UWEC s incoming freshmen. Guida 8

College Advanced Aged Degrees/Total Students/Distance from From Eau UWEC Claire UWEC UW Campuses Grad_Degrees/Dist 0.0-0.9 0.9-0.66 0.66-1.11 1.11-2.32 2.32-5.5 5.5-1.12 1.12-36.95 36.95-97.7 97.7-259.63 259.63-690.72 Figure 7 Conclusion Results using a gravity model approach to find origins of UWEC students. More students come from closer distances and those that don t are usually from higher population areas. When looking at the formula, there is strong correlation between the statistics and all maps produced. Intervening opportunities at other UW schools keep the numbers lower from areas further away and higher in the counties surrounding Eau Claire. Students ask themselves why travel a greater distance if the same of similar opportunities are closer in proximity. Tobler s First Law says closer things are more related than distant and that is definitely true when mapping origins of UWEC students. Those populations closer to Eau Claire are much more likely to have similar demographics and less intervening opportunity to choose a different UW school outside of the area. The distance, or space as separation, clearly seems to be the controlling factor when analyzing the origin of UWEC students. Guida 9

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