 Hello, my name is Miranda. This is Melissa, Alice, Ethan, and Maddie. We partner with the City of Grand Rapids on a project that is aimed at keeping people in their homes. So Grand Rapids is consistently one of the top five developing cities in the United States. With this growth, we have seen an increase in housing rates to the point that long-term residents are no longer able to afford their rent. And a factor that is adding to this displacement is that financial need in the city is not being accurately assessed or managed. To further explore this issue, we looked at four neighborhoods, Westside Connection, West Grand, John Paul Park, and Swan. This project is important first and foremost because people that have been residents of the city for decades are being forced out of the community that they love. We saw this firsthand when we took a tour of the city's Westside with Commissioner Herbert Hart. We saw that development in South is not the issue, but the fact that development is being implemented in a way that is not either of a use of space or conscious of the economic climate of the communities that they're being implemented in. This project has the power to influence policy and development in a way that allows the city to keep its color and character. It also has the power to influence development in a way that promotes a women's situation where development can still be encouraged, but in a way that positively impacts the community and promotes diversity. So to begin, we had a wealth of publicly available data from many different sources, and our task was to pare down that information to find variables that we thought would best paint a picture or displacement. We initially considered building a model for displacement, but quickly learned that with the data available, it would be difficult to determine forced displacement rather than voluntary location. We eventually decided that the variables that would best paint this picture were demographics, housing costs, and income. We also decided to address the separate but related issue of income by finding means to find median income for these neighborhoods to best paint a picture of the city's financial landscape. So like we're going to mention, the large part of this project was looking at area median income, or AMI, and this figure is used as a benchmark to assess financial aid and housing market rates. And the issue close to us is that the current figure used by the city comes from the Department of Housing and Urban Development, or HUD as well referred to it, and that number is around 69,900 as of 2018. And that number is high to skew because it includes wealthier neighborhoods like ADA and Eastern Rapids. So our task was to try and narrow the scope of AMI down to smaller areas like the four neighborhoods on the west side. And our analysis has shown much lower AMI levels that have gradually increased but only by a small margin, more in the $35,000 to $55,000 range. So as you're seeing the disparity between our target west side neighborhoods and the HUD AMI, we decided it would be a good idea to run a program on the entire city of Grand Rapids, which is represented by deep orange neighborhoods on the right. And we found that the HUD AMI was about $25,000 more than the AMI of Grand Rapids, which is represented by HUD AMI represented by this whole map. And it's clear that HUD AMI is not represented by Grand Rapids accurately. And so when we decided we were going to make this income finder, we had some goals in mind. The first goal was to make a program that you could simply upload in an American community survey, especially your income data too, along with some census tracks which represent neighborhoods, and have a program that would just give immediate income for that area or for those areas. And then after we got that to work, we wanted the program to just make changes to the easiest file format. And so to do so, we wrote the program to recognize key words and extrapolate that directly from the spreadsheet. And then our last goal was to find a school that would be easy to upload to GR data, community platforms. So we wrote it in Python, which is a program that anyone should have things to do. So going a little more depth on how our program works, this top image is of an ACS data sheet when it's first read into our program. And it's kind of messy and there's some unnecessary things that we drop out. But the main feature of our program is reading through this geography column and pulling out the census tracks to create a new index down here for the new gap, right? So that makes it super easy to pull out the rows of data that we need corresponding to what the user inputs. And then we also read through these column headers to pull out income ranges and turn them into much easier numbers to work with up here. And then once we calculate population median, based on the range that falls, then we can turn it into an actual income figure. So to kind of recap our AMI analysis, we found that AMI levels to be much lower than the HUD AMI, more than $35,000 to $55,000 range. And that can have great consequences when we're assessing financial aid in these neighborhoods. So to investigate the extent of displacement that's happening within our four-target neighborhoods of Swan, John Loughard, West Side Connection, and West Grand, we decided to analyze time series data for variables such as median rent values, which we got from Zillow, median income, which we found using that program that we created, as well as demographic data, such as total population, white population, and people of color population from ACS. And one of our major findings was that in all four neighborhoods, people of color are moving out. And in this image, you can see particularly from 2012 to 2013, there's a very drastic decrease in the people of color population, where 40 to 50% of people of color in those neighborhoods moved out during that time period. And such a sudden change in a short period of time indicates that these people were displaced rather than choosing to voluntarily move. And in the years since then, the numbers of the people of color in that neighborhood have not risen back to those numbers seen in 2012. And then another fine day from our time series data was that while median income has fluctuated a bit from neighborhood to neighborhood, on average, I had been fairly stagnant, whereas rent values in these neighborhoods has been steadily increasing since 2013. And looking at rent as a percent of monthly median income in these neighborhoods, we saw that in particular in the neighborhood of West Grand, this percent rose by 8% and in Swam, or it was 10% West Grand and 8% in Swam. So those people of color that were displaced from their neighborhoods may be because they can no longer afford to live there, are very unlikely to be moved back to the places that they call home because it's continued to get more expensive since then. And then to dig deeper into the displacement that we were seeing, we created a program in SAAS that would run cross-correlations between our time series variables. And cross-correlation is a statistical method that measures the similarity between variables and time series data, where if there's a strong positive correlation, that means that the two variables change similar to each other, either both increasing or decreasing. And if there's a strong negative correlation, that means that the two variables change opposite to each other, where when we see an increase in one, we tend to see an increase in the other. And cross-correlation also tests to see if there's a time lag between when we see changes in our data by shifting one of the variables either forward or backwards in time. And at the bottom, we have some examples of what a negative correlation, a positive correlation, and a time lag in time series data look like. So our results from these cross-correlations was that one of them was that there's a very strong negative correlation between white population and people of color population in all four of our neighborhoods. And there's no timeline between maps, so that means that when we see an increase in one population, we tend to also see a decrease in the other population at the same time. And another one of our findings was that there's a very strong positive correlation between the white population and needing income in most of our neighborhoods with no timeline between them. So when we see an increase in one of those, we also tend to see an increase in the other at the same time and same for decrease. But one caveat for our findings is that we only had eight observations per variable in our time series data, one per year from 2010 to 2017. So there was a large error associated with these correlations I've found. However, when we go on to plot the data, we see that these correlations become quite evident. So here you can see the total population, white population and people of color population in each of our four neighborhoods. And you can clearly see that negative correlation between the white population and people of color population and how they're changing opposite to each other over time. So like how we saw that drastic decrease in the people of color population from 2012 to 2013, there's also significant increase in the white population in all four neighborhoods as well. And also notice how the total population has not changed too much over time. So as people are moving out of these neighborhoods and white people are moving in, we're seeing a decrease in the diversity of these neighborhoods. And then here we have the white population and the median income out of our four neighborhoods. And you can see the positive correlation most prominently in John Hart and Swan. And it's also very much that connection, but we did not see that correlation in us grand. But overall, those four neighborhoods, when there's an increase in white population, we tend to see an increase in the median income as well. A couple of this with the fact that we're seeing people of color moving out of these neighborhoods indicates that there's a very strong economic reason behind why we're seeing a displacement of people of color. So in conclusion, the big problem that you're trying to tackle here was the involuntary displacement of people in lower income brackets. The city has a lot of opportunities to make sure that both development and assistance occurs in a responsible and equitable manner. One of these things would be using a smaller median income to assess the needs of individuals in these target neighborhoods. This need may need to be reassessed over time, but we're now, let's see how we're at. Since the semester's only so long, we couldn't look at everything that we found at 16. So if you were to pick this project back up, some variables of interest might be water shutouts, building permits, changes in age demographics, and the percentage of the population spending more than 30% of their income on rent. Second, it would be interesting to characterize low, medium, and high-risk areas in terms of displacement. Finally, we'd like to say thank you to some people who made this project possible, our advisor, Dr. Austin, our advisors with the city, and finally, pick math of the Mathematical Association of America and the National Science Foundation For more information on Mathematical Association of America and the National Science Foundation visit www.mathematical.org