Jerry Shannon
dollar_data <- st_read("data/geog4300_dollarstoredata.gpkg")## Reading layer `geog4300_dollarstoredata' from data source `C:\Users\samsh\OneDrive\Documents\Productivity\College\GEOG4300 Data Science in GIS\Final Project\geog4-6300--final-project-SamShuster97\data\geog4300_dollarstoredata.gpkg' using driver `GPKG'
## Simple feature collection with 2080 features and 15 fields
## geometry type: MULTIPOLYGON
## dimension: XY
## bbox: xmin: -88.8223 ymin: 40.88782 xmax: -87.02687 ymax: 42.63946
## geographic CRS: WGS 84
focused_data_sf<-dollar_data%>%
select(totpop, white_pct, afam_pct, pov_pct, dt_dist)
focused_data<-dollar_data%>%
as_tibble()%>%
select(totpop, white_pct, afam_pct, pov_pct, dt_dist)Use this template for your responses for the final project.
In the space below, list the four variables you are using for this analysis. The dependent variable should be one of the measures of dollar store proximity. Explain why you’re choosing each variable–what association do you think they might have with dollar store proximity? Finally, write a research question that will be answered through your analysis.
I will be conducting my analysis using: * pov_pct: % of people with
household incomes below poverty level * white_pct: % of people
classified White, non-Hispanic * afam_pct: % of people classified
African-American, non-Hispanic * dt_dist: Distance to the closest
Dollar Tree in m
I chose to use the pov_pct variable because I think it will provide insight on how income influences corporate decision making pertaining to the selection of new store locations as well as what sorts of demographics are targeted in particular. Secondarily but also quite important - modeling using this variable will highlight fiscal inequities between race demographics in the region. I hypothesize that higher income areas will have more dollar trees than lower income areas.
The afam_pct variable was chosen in order to test whether dollar trees are established in any discernible way according to racial distribution, specifically, “Do stores open more or less frequently in areas with high-percentage African-American populations?” I hypothesize that areas of with high percentages of African-Americans will have fewer dollar trees than predominantly white areas (10% or more African-American)
The dt_dist variable was chosen as the dependent variable that will be used to test correlation and regression between the previously mentioned variables. This variable will provide insight pertaining to the distribution of all dollar trees according to the above variables. Testing only one particular chain will highlight any inequities in how the corporation chooses where it will establish stores.
Research Question 2: Does the Dollar Tree franchise establish stores in particular areas with increased frequency based on its constituent income and/or race demographics?
Null hypothesis 1: there is a significant statistical bias towards store establishment in particular areas based on race. Null hypothesis 2: there is a significant statistical bias towards store establishment in particular areas based on income. Alternative hypothesis 1: there is no statistical bias towards store establishment in particular areas based on race. Alternative hypothesis 2: there is a significant statistical bias towards store establishment in particular areas based on income
Describe the central tendency (e.g., mean, median, mode), statistical distribution (e.g., standard deviation and/or IQR), normality, and spatial distribution of each variable using the techniques we have covered in class. Describe any notable patterns you see in these variables based on this analysis.
Central Tendency and basic Statistics:
mean_pov_pct<-round(mean(focused_data$pov_pct, na.rm = TRUE), digits = 2)
median_pov_pct<-median(focused_data$pov_pct, na.rm=TRUE)
mean_wht_pct<-round(mean(focused_data$white_pct, na.rm = TRUE), digits = 2)
median_wht_pct<-round(median(focused_data$white_pct, na.rm=TRUE), digits = 2)
mean_afam_pct<-round(mean(focused_data$afam_pct, na.rm = TRUE), digits = 2)
median_afam_pct<-round(median(focused_data$afam_pct, na.rm=TRUE), digits = 2)The mean percentage of people under the poverty line is 15.09% and the median is 10.7%. The mean percentage of people who are white is almost half, with a value of 48.94% and a median of 55.4%. The mean percentage of people who are African-American is 21.37% with a median value of 4.6%.
ggqqplot(dollar_data$white_pct, title = "Percent White", color = "darkslategrey", xlab = "Theoretical", ylab = "Sample")
hist(dollar_data$white_pct)
wilcox.test(dollar_data$white_pct, dollar_data$white_pct)##
## Wilcoxon rank sum test with continuity correction
##
## data: dollar_data$white_pct and dollar_data$white_pct
## W = 2163200, p-value = 1
## alternative hypothesis: true location shift is not equal to 0
model_pov = lm(dt_dist~pov_pct, data = dollar_data)
summary(model_pov)##
## Call:
## lm(formula = dt_dist ~ pov_pct, data = dollar_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3325 -1556 -591 686 39160
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3587.560 91.210 39.33 <2e-16 ***
## pov_pct -44.361 4.588 -9.67 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2708 on 2077 degrees of freedom
## (1 observation deleted due to missingness)
## Multiple R-squared: 0.04308, Adjusted R-squared: 0.04262
## F-statistic: 93.5 on 1 and 2077 DF, p-value: < 2.2e-16
plot(model_pov)
Based on the QQ plot and histogram for the white_pct variable, the data is not normally distributed. It is skewed both positively and negatively which indicates that there is no definitive correlation that can be extrapolated only given the two variable tested (white_pct and dt_dist). The positive skew may indicate that there is a tendency for stores to be established in areas that are not predominantly white. Conversely, the opposite could be said concerning the negative skew - stores tend to be established in predominantly white areas. Given this mixed interpretation, there does not seem to be an obvious statistical correlation between the two variables.
ggqqplot(dollar_data$afam_pct, title = "Percent Black", color = "slateblue", xlab = "Theoretical", ylab = "Sample")
hist(dollar_data$afam_pct)
wilcox.test(dollar_data$afam_pct, dollar_data$afam_pct)##
## Wilcoxon rank sum test with continuity correction
##
## data: dollar_data$afam_pct and dollar_data$afam_pct
## W = 2163200, p-value = 1
## alternative hypothesis: true location shift is not equal to 0
model_wht = lm(dt_dist~white_pct, data = dollar_data)
summary(model_wht)##
## Call:
## lm(formula = dt_dist ~ white_pct, data = dollar_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3876 -1444 -412 743 37884
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1410.236 104.631 13.48 <2e-16 ***
## white_pct 30.836 1.796 17.17 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2590 on 2078 degrees of freedom
## Multiple R-squared: 0.1243, Adjusted R-squared: 0.1238
## F-statistic: 294.8 on 1 and 2078 DF, p-value: < 2.2e-16
plot(model_wht)
The QQ plot and histogram for the afam_pct variable has a similar pattern to the white_pct variable, however, the magnitude of observations plays an important part in interpretation. There is a strong positive skew which may indicate that Dollar Trees tend to be opened more frequently in areas that are primarily occupied by African-Americans. However, the strong negative skew may refute that claim. No definitive interpretation can be made based on these figure alone.
ggqqplot(dollar_data$pov_pct, title = "Poverty Percentage", color = "orange", xlab = "Theoretical", ylab = "Sample")## Warning: Removed 1 rows containing non-finite values (stat_qq).
## Warning: Removed 1 rows containing non-finite values (stat_qq_line).
## Warning: Removed 1 rows containing non-finite values (stat_qq_line).
hist(dollar_data$pov_pct)
wilcox.test(dollar_data$pov_pct, dollar_data$pov_pct)##
## Wilcoxon rank sum test with continuity correction
##
## data: dollar_data$pov_pct and dollar_data$pov_pct
## W = 2161121, p-value = 1
## alternative hypothesis: true location shift is not equal to 0
model_blk = lm(dt_dist~afam_pct, data = dollar_data)
summary(model_blk)##
## Call:
## lm(formula = dt_dist ~ afam_pct, data = dollar_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3203 -1565 -601 738 38820
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3292.317 71.280 46.189 <2e-16 ***
## afam_pct -17.461 1.843 -9.475 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2710 on 2078 degrees of freedom
## Multiple R-squared: 0.04141, Adjusted R-squared: 0.04095
## F-statistic: 89.77 on 1 and 2078 DF, p-value: < 2.2e-16
plot(model_blk)
There is a strong positive skew for the pov_pct variable which indicates that stores may in fact be established with increased frequency in low income areas. Significant finding.
The p-value in this case is far smaller than 0.05 which means it is statistically significant enough to accept the null hypothesis. Therefore, we reject the null hypothesis and accept the alternative hypothesis in this particular case. The household data from the two cities does not differ significantly.
ggqqplot(dollar_data$dt_dist, title = "Dollar Tree Dist", color = "chartreuse2", xlab = "Theoretical", ylab = "Sample")
hist(dollar_data$dt_dist)
shapiro.test(dollar_data$dt_dist)##
## Shapiro-Wilk normality test
##
## data: dollar_data$dt_dist
## W = 0.67405, p-value < 2.2e-16
#lq_dollar_data = dollar_data %>%
# mutate(dt_lq = n(dt_dist)/2080)
#dollar_data_ll <- st_transform(dollar_data, "+proj=longlat +ellps=WGS84 +datum=WGS84")tm_shape(dollar_data)+
tm_fill("medinc", style = "fisher")+
tm_borders()+
tm_basemap(server="OpenStreetMap",alpha=0.5)
tm_shape(dollar_data)+
tm_fill("medinc", style = "fisher", palette="-RdBu")+
tm_borders()+
tm_basemap(server="OpenStreetMap",alpha=0.5)
The medinc variable was mapped in order to gain a more in-depth understanding of how stores might be distributed. This is not a necessary component of the study but was done despite that.
tm_shape(dollar_data)+
tm_fill("pov_pct", style = "fisher")+
tm_borders()+
tm_basemap(server="OpenStreetMap",alpha=0.5)
The above map shows the distribution of the percentage of people below the poverty line. Darker colors indicate more impoverished areas. The most impoverished areas appear to be in the eastern-most and the south-central areas with other hot-spots dotted around the perimeter of the city.
tm_shape(dollar_data)+
tm_polygons("white_pct", style = "fisher")+
tm_basemap(server="OpenStreetMap",alpha=0.5)
tm_shape(dollar_data)+
tm_polygons("white_pct", style = "fisher", palette="-RdBu")+
tm_basemap(server="OpenStreetMap",alpha=0.5)
The above show the spatial distribution of areas with varying percentages of people living within them classified as white. Two different color schemes are used for clarity. The city center appears to be a rather diverse area, although it appears as though few white people live in the south-central area. There is significant homogeneity the further one travels from the city center/the eastern border of the city.
tm_shape(dollar_data)+
tm_polygons("afam_pct", style = "fisher")+
tm_basemap(server="OpenStreetMap",alpha=0.5)
tm_shape(dollar_data)+
tm_polygons("afam_pct", style = "fisher", palette="RdBu")+
tm_basemap(server="OpenStreetMap",alpha=0.5)
The above show the spatial distribution of areas with varying percentages of people living within them classified as African-American. Two different color schemes are used for clarity. The south-central portion of the city appears to be primarily inhabited by African-Americans. An overwhelming majority of African-Americans living in the city live within the South-central area.
tm_shape(dollar_data)+
tm_polygons("dt_dist", breaks=c(0,500,1000,3000,5000,7000,10000,50000))
Based on the maps created above, we can see that the further one travels from the Eastern edge of the city (which is essentially the city center), we see that dollar tree distances increase. This indicates that Dollar Trees are predominantly located within the city center. The classification breakdown is as such: 0-0.5km, 0.5-1km, 1-3km, 3-5km, 5-7km, 7-10km, and 10-50km. This resolution of analysis takes transportation into consideration. Given the nature of the study, access to stores is incumbent upon the ability to travel to a location. Those who are not financially privileged are limited by distance so stores within walking distance are the most accessible.
There is no obvious trend in store distribution based on race alone. The majority of stores tend to be located well within the bounds of the city limits, predominantly occupying the central portion of the city. Given the diversity of the city center, no obvious bias towards establishing stores areas based on race.
Create a multivariate regression model that assesses the relationship between your independent and dependent variables. Check for multicollinearity and the potential effect of outliers. Also check whether the residuals have a random distribution both statistically and spatially. Discuss what model diagnostics tell you about the validity of the model.
model_multivar = lm(dt_dist~pov_pct + white_pct + afam_pct, data = dollar_data)
summary(model_multivar)##
## Call:
## lm(formula = dt_dist ~ pov_pct + white_pct + afam_pct, data = dollar_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3996 -1431 -376 731 37625
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 550.803 233.508 2.359 0.0184 *
## pov_pct 16.207 6.612 2.451 0.0143 *
## white_pct 40.475 2.919 13.866 <2e-16 ***
## afam_pct 6.667 2.624 2.541 0.0111 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2581 on 2075 degrees of freedom
## (1 observation deleted due to missingness)
## Multiple R-squared: 0.1315, Adjusted R-squared: 0.1302
## F-statistic: 104.7 on 3 and 2075 DF, p-value: < 2.2e-16
plot(model_multivar)
mv_residuals = residuals(model_multivar)
summary(mv_residuals)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -3995.6 -1431.2 -375.8 0.0 731.4 37624.5
ggqqplot(mv_residuals, title = "Multivariate Regression Model", xlab = "Theoretical", ylab = "Sample")
vif(model_multivar)## pov_pct white_pct afam_pct
## 2.286264 2.660467 2.235622
bptest(model_multivar)##
## studentized Breusch-Pagan test
##
## data: model_multivar
## BP = 51.21, df = 3, p-value = 4.412e-11
Based on your results, interpret the results of your model, focusing on the direction, magnitude, and significance of each variable and the overall power of the model. Based on this analysis, what answer can you give to your research question? What limitations or problems does your analysis have that should be addressed in the future?
The QQ plot of residuals indicates a strong skew which is to be expected from non-parametric data, however, the plot is mostly normal which indicates that the variables used are effective for statistical analysis. The skew is strongly in the negative direction with some high outliers at the upper end of the distribution.
Based on early findings alone, my hypothesis could not be supported. Based on the multiple R-squared value, only 13% of the variation in the model can be explained by these variables. From the multivariate regression model, a statistically significant level of correlation is supported between the variables assessed and store location establishment. That said, the R-squared value is not particularly large so this model may not be the best fit. The most influential variable appears to be white_pct. The model is most heavily influenced by this variable, indicated by the highly significant p-value. This is likely in part because of the large white population in the city, which subsequently may have skewed the model. The statistical significance could be mere coincidence as a result. The p-values for the other two variables are still statistically significant but to a lesser degree. They still support both null hypotheses given their significance. Somewhat surprisingly, the impoverished areas did not have greater or diminished access to the Dollar Trees.
The multiple R-squared is 0.1315 while the Adjusted R-squared is 0.1302. The lack of change in the adjusted R-squared indicates that the statistical significance is illusory.
Results from vif test returned a value less than 4 which indicates a low level of multicollineraity.
Ultimately, we can conclude that this model does not statistically prove a bias towards the establishment of Dollar Trees in particular areas based on race or income. Despite significant p-values and a seemingly significant model, the fact that the adjusted R-squared variable is smaller than the un-adjusted indicates misleading results. I think one limitation of this analysis was the absence of point data explicitly detailing store locations. I think that data would have been helpful for providing an even finer resolution to conduct analysis. Additionally, a longer list of variables to chose from to conduct the analysis might have offered unexpected yet significant findings - some examples might include zoning classification data or proximity to certain infrastructure features like bus or train stations. As far as my individual analysis goes, I feel i was somewhat limited in my ability to create visualizations. In future, I would include figures like a kernel density map.