Regression Analysis of Crime in Seattle
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Ryan Grammer
GIST 602B
Problem Statement
Crime is a problem that all large cities in the United States face, whether it be property crimes such as theft and vandalism, or violent crimes such as assault. Some areas of a city are more susceptible to crime than other areas. Can we attribute the crime in Seattle with a factor such as median household income, median home value, the unemployed population, or the population who have attained a high school diploma?
Crime is a problem that all large cities in the United States face, whether it be property crimes such as theft and vandalism, or violent crimes such as assault. Some areas of a city are more susceptible to crime than other areas. Can we attribute the crime in Seattle with a factor such as median household income, median home value, the unemployed population, or the population who have attained a high school diploma?
Data
The study area of this analysis is the city of Seattle. Seattle is the most populous city in the state of Washington and the 18th most populous city in the United States. According to City Data, Seattle's crime index is 2.2 times greater than the U.S. average. We will use census tracts in Seattle to complete this analysis.
The study area of this analysis is the city of Seattle. Seattle is the most populous city in the state of Washington and the 18th most populous city in the United States. According to City Data, Seattle's crime index is 2.2 times greater than the U.S. average. We will use census tracts in Seattle to complete this analysis.
The data used in this analysis is broken down by census tract in the city of Seattle. The data includes fields such as crime index, median household income, median home value, population density, the unemployed population percentage, and the population who have attained a high school diploma percentage.
The data used in this analysis is broken down by census tract in the city of Seattle. The data includes fields such as crime index, median household income, median home value, population density, the unemployed population percentage, and the population who have attained a high school diploma percentage.
Map of the study area
Metadata table
Methods
The projection that I used for this data is NAD 1983 HARN State Plane Washington North FIPS 4601 (Meters). Washington is split in half horizontally by the State Plane system (North/South). Seattle falls in the north region of the State Plane coordinate system. This projection covers the entire northern part of the state of Washington and is the standard for King County (the county Seattle is located in). This projected coordinate system works well to minimize distortion in large scale maps such as the city of Seattle.
The projection that I used for this data is NAD 1983 HARN State Plane Washington North FIPS 4601 (Meters). Washington is split in half horizontally by the State Plane system (North/South). Seattle falls in the north region of the State Plane coordinate system. This projection covers the entire northern part of the state of Washington and is the standard for King County (the county Seattle is located in). This projected coordinate system works well to minimize distortion in large scale maps such as the city of Seattle.
My dependent variable is Crime Index. My dependent variables are median household income, median home value, population density, unemployed population percentage, and the population who have attained a high school diploma percentage.
My dependent variable is Crime Index. My dependent variables are median household income, median home value, population density, unemployed population percentage, and the population who have attained a high school diploma percentage.
Ordinary Least Squares regression analysis is a regression method that minimizes the sum of the squared differences between observed and estimated values. This method provides a global model of the dependent variable. It creates a single regression equation to represent the correlation between the explanatory variables and the dependent variable. There are six different checks that OLS regression goes through to ensure that the model meets the standards required for analysis.
Ordinary Least Squares regression analysis is a regression method that minimizes the sum of the squared differences between observed and estimated values. This method provides a global model of the dependent variable. It creates a single regression equation to represent the correlation between the explanatory variables and the dependent variable. There are six different checks that OLS regression goes through to ensure that the model meets the standards required for analysis.
Exploratory regression analysis is used to find the best Ordinary Least Squares regression by trying all possible combinations of explanatory variables. By exhausting all options, this method will find the models that best represent the relationship between the explanatory variables and the dependent variable. It provides a summary of the top models, as well as the top passing models (models that pass the OLS specifications).
Exploratory regression analysis is used to find the best Ordinary Least Squares regression by trying all possible combinations of explanatory variables. By exhausting all options, this method will find the models that best represent the relationship between the explanatory variables and the dependent variable. It provides a summary of the top models, as well as the top passing models (models that pass the OLS specifications).
Ordinary Least Squares (OLS) Geoprocessing Tool (ArcGIS Pro)
Exploratory Regression Geoprocessing Tool (ArcGIS Pro)
The Geographically Weighed Regression (GWR) analysis is a regression method that fits a regression for each feature. Instead of creating a single regression equation like OLS, this method creates regression equations for each feature using its neighbors to represent the correlation between the explanatory variables and the dependent variable. This method provides a local model of the dependent variable that accounts for nonstationarity. This method is used when a the Koenker test statistic has statistically significant nonstationarity.
The Geographically Weighed Regression (GWR) analysis is a regression method that fits a regression for each feature. Instead of creating a single regression equation like OLS, this method creates regression equations for each feature using its neighbors to represent the correlation between the explanatory variables and the dependent variable. This method provides a local model of the dependent variable that accounts for nonstationarity. This method is used when a the Koenker test statistic has statistically significant nonstationarity.
The relationship between the Crime Index and the explanatory variables is not nonstationary as the values from the Koenker test statistic are not statistically significant.
The relationship between the Crime Index and the explanatory variables is not nonstationary as the values from the Koenker test statistic are not statistically significant.
Geographically Weighted Regression (GWR) Geoprocessing Tool (ArcGIS Pro)
In the Exploratory Regression Analysis, I have set the minimum number of explanatory variables to 1 and the maximum number of explanatory variables to 5 (max). I chose this range of explanatory variables to ensure that all models that are possible are tested. I have chose to leave all of the other values in the search criteria as the default. In the Geographically Weighted Regression, I have left the model type as the default (Continuous (Gaussian)). For the neighborhood type, I selected Number of Neighbors to ensure that each feature has the same number of neighbors. For the neighborhood selection method, I selected Golden search as it "determines the distance or number of neighbors with the lowest AICc as the neighborhood size by finding the maximum and minimum distances and testing the AICc at various distances incrementally between them" (Esri).
In the Exploratory Regression Analysis, I have set the minimum number of explanatory variables to 1 and the maximum number of explanatory variables to 5 (max). I chose this range of explanatory variables to ensure that all models that are possible are tested. I have chose to leave all of the other values in the search criteria as the default. In the Geographically Weighted Regression, I have left the model type as the default (Continuous (Gaussian)). For the neighborhood type, I selected Number of Neighbors to ensure that each feature has the same number of neighbors. For the neighborhood selection method, I selected Golden search as it "determines the distance or number of neighbors with the lowest AICc as the neighborhood size by finding the maximum and minimum distances and testing the AICc at various distances incrementally between them" (Esri).
Results
The top three models in this analysis are all non passing models. All three models have an adjusted R square value of 0.13. However, the difference between the models is the AICc value, with the lower value being considered a better model.
The top three models in this analysis are all non passing models. All three models have an adjusted R square value of 0.13. However, the difference between the models is the AICc value, with the lower value being considered a better model.
The top model has an adjusted R square value of 0.13, meaning that median household income, high school diploma percentage, and unemployed population percentage explains 13 percent of the crime index. The AICc value is 2313.13, which represents the best model, hence why we chose this model. The Jarque-Bera p-value is statistically significant here since it has a low p-value, which means that our model is biased. Our Koenker (BP) Statistic on the other hand is not statistically significant as we observe a high p-value, meaning the model is not heteroskedastic. Our VIF value tells us that there is no multicollinearity in the model since the value is < 7.5.
The top model has an adjusted R square value of 0.13, meaning that median household income, high school diploma percentage, and unemployed population percentage explains 13 percent of the crime index. The AICc value is 2313.13, which represents the best model, hence why we chose this model. The Jarque-Bera p-value is statistically significant here since it has a low p-value, which means that our model is biased. Our Koenker (BP) Statistic on the other hand is not statistically significant as we observe a high p-value, meaning the model is not heteroskedastic. Our VIF value tells us that there is no multicollinearity in the model since the value is < 7.5.
The Geographically Weighted Regression analysis tested 12 different numbers of neighbors. The analysis settled on 39 neighbors from the Golden Search method. The AICc of the model is 2239.88, better than the Exploratory Regression Analysis, but still not the best. The method's adjusted R square value was 0.5281, meaning that median household income, high school diploma percentage, and unemployed population percentage explains 52 percent of the crime index.
Population Density Coefficient from GWR Analysis
We can see from the Population Density Coefficient map that the coefficients for the southern section of the map are negative, meaning have a negative influence in the models equation. This means that the estimated crime index will drop as the population density increases. The opposite is true for the northern section.
We can see from the Population Density Coefficient map that the coefficients for the southern section of the map are negative, meaning have a negative influence in the models equation. This means that the estimated crime index will drop as the population density increases. The opposite is true for the northern section.
Median Home Value Coefficient from GWR Analysis
We can see from the Median Home Value Coefficient map that the coefficients for the downtown section of the map are positive, meaning they have a positive impact in the models equation. This means that the estimated crime index will increase as the median home value increases. The opposite is true for the areas farther from the downtown area.
We can see from the Median Home Value Coefficient map that the coefficients for the downtown section of the map are positive, meaning they have a positive impact in the models equation. This means that the estimated crime index will increase as the median home value increases. The opposite is true for the areas farther from the downtown area.
Conclusion
From the Explanatory Regression analysis, we found that there were no passing models. All of the models tested had an adjusted R square value of 0.13 or lower. The top model had that median household income, high school diploma percentage, and unemployed population percentage explains only 13 percent of the crime index. We also saw that the Jarque-Bera p-value is statistically significant here meaning that our model is biased. Even though our Koenker (BP) Statistic told us that the model is not heteroskedastic and our VIF value told us that there is no multicollinearity in the model, there is not a good way to attribute Crime Index to any of our dependent variables.
From the Explanatory Regression analysis, we found that there were no passing models. All of the models tested had an adjusted R square value of 0.13 or lower. The top model had that median household income, high school diploma percentage, and unemployed population percentage explains only 13 percent of the crime index. We also saw that the Jarque-Bera p-value is statistically significant here meaning that our model is biased. Even though our Koenker (BP) Statistic told us that the model is not heteroskedastic and our VIF value told us that there is no multicollinearity in the model, there is not a good way to attribute Crime Index to any of our dependent variables.
From the Geographically Weighted Regression analysis, we found that the model's adjusted R square value was 0.5281, meaning that median household income, high school diploma percentage, and unemployed population percentage explains 52 percent of the crime index. However, the Jarque-Bera p-value is statistically significant here meaning that our model is biased, meaning that we cannot take the results of the GWR analysis as significant.
The limitations of this analysis are that the data was biased, and did not allow for any passing models. In order to have a model that passes, all 6 requirements must be met, and since one failed, it cost us as our analysis was not able to define a method that would work. In another analysis, I would try to consider more explanatory variables that would extend the analysis and hopefully find a passing model that attributes the explanatory variables to the Crime Index.
The limitations of this analysis are that the data was biased, and did not allow for any passing models. In order to have a model that passes, all 6 requirements must be met, and since one failed, it cost us as our analysis was not able to define a method that would work. In another analysis, I would try to consider more explanatory variables that would extend the analysis and hopefully find a passing model that attributes the explanatory variables to the Crime Index.
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