1 The United States of America’s Poverty Rate: A Final Project Theresa Mai Department of Statistics, Oregon State University ST 352: Introduction to Statistical Methods II Dr. Jeffrey Kollath June 9, 2020 2 The United States of America’s Poverty Rate Question of Interest & Motivation In 2018, the United States of America faced backlash by the United Nations’ Special Rapporteur on extreme poverty and human rights, and the resulting report brought great concern regarding the United States’ status as one of the big players in international politics. From the Special Rapporteur’s visit in the U.S., the UN found that about 40 million people live in poverty, another 18.5 million live in extreme poverty, and 5.3 million live in absolute poverty even if the United States is one of the wealthiest countries in the world (Alston, 2018). Even though the U.S. is focused on being internationally involved in politics, the country has its own issues that need to be addressed domestically. Because of this need for action, I decided to use this final project as an opportunity to research what factors impact poverty rates in the United States, using a random sample of 40 states. For this project, my question of interest is “Does at least one of the following factors (percentage of population being of color, high school graduation rate, median household income, percentage of households being food-insecure, cost of living index, natural environment quality, and healthcare quality) have an effect on poverty rates in a state?” I chose these explanatory variables because there is a broad understanding that there are systemic barriers that people face in order to overcome poverty. Sometimes, this can be hard to avoid due to where they come from in terms of socioeconomic status and ethnicity, especially when communities in the USA are created through environmental racism (Frederick, 2018; Newkirk II, 2018). This is why the explanatory variables percentage of population being of color, percentage of households being food-insecure, natural environment quality, and healthcare quality are chosen. Even so, there are 3 ways to try to get to the middle class by pursuing further education and a decent paying job, which explains why high school graduation rates, median household income, and cost of living index are included. Data Collection I chose to obtain my data from two primary sources: the U.S. News & World Report and the U.S. Census Bureau (United States Census Bureau, n.d.; U.S. News & World Report, n.d.). Through the U.S. Census Bureau, I collected data on the explanatory variable percentage of population being of color for each state in 2019, and this explanatory variable is calculated by subtracting the percentage of the population being white (only) from 100%. For the rest of the explanatory variables and response variable, I collected data from the U.S. News & World Report’s data explorer for 2018. Assessment of Conditions 4 Now, one question that may come in mind is how representative the sample is. Since the states in the U.S. were chosen randomly, we are confident that the resulting sample we used is representative of the population, which is the states of the U.S.A. Another condition is all observations being independent of each other. Since the sample was chosen randomly and data was collected for each state, which is governed by the federal, state, and local government, we are confident that there are no dependencies between each case. Looking at the scatterplot matrix, we can see several explanatory variables that seem to have a strong relationship with each other (median household income, % food-insecure households, cost of living index, and healthcare quality). By looking at the correlation matrix, we found out that none of these explanatory variables are highly correlated. This means our model meets the multicollinearity condition without any concerns. For the outlier condition, there seems to be several outliers, like Mississippi with healthcare quality and percentage of food-insecure households. Plus, Nevada has the lowest high school graduation rate, and there are several other outliers as well. Even so, since the sample of states is representative of the population, we cannot remove the outliers. 5 For the linearity condition, looking at the scatterplot matrix, we can see that environment quality and the percentage of the population being of color could possibly have a nonlinear relationship with the response variable, the poverty rate. To verify, looking at the residual plot of residuals versus predicted values, we can see that there is no significant curve, so we are somewhat confident in believing that the linearity condition is met. Looking at the constant variation condition, we can see that it is relatively met due to seeing the points being spread out, with some outliers, in the residual plot of residuals versus predicted values. For the normality condition, we can see it is met because in the normal probability plot of the residuals, we can see that the residuals fall mostly on or near the line. Finally, is a transformation needed for this model? Not necessarily. Without any transformations, the model met all the needed conditions, which removes the need to turn to other models with transformations. Even if we did do transformations, it did not change our resulting model and its ability to meet the conditions for multiple linear regression. Therefore, we are fine with our current model with no transformations. Analysis & Discussion When doing the F-test for this model in addition to the t-tests for each explanatory variable, below is the given output: Call: lm(formula = poverty ~ poc + graduation + income + hunger + col + environment + healthcare, data = final) Residuals: 6 Min 1Q Median 3Q Max -1.3491 -0.6533 -0.1592 0.6479 2.4352 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 2.132e+01 4.835e+00 4.410 0.000109 poc 1.003e-01 2.627e-02 3.818 0.000583 graduation -5.343e-02 3.337e-02 -1.601 0.119150 income -2.563e-04 4.229e-05 -6.062 9.08e-07 hunger 3.699e-01 1.410e-01 2.623 0.013225 col 2.624e-02 2.386e-02 1.100 0.279581 environment -7.062e-03 1.001e-02 -0.706 0.485478 healthcare 4.140e-02 2.563e-02 1.615 0.116024 Residual standard error: 1.004 on 32 degrees of freedom Multiple R-squared: 0.8952, Adjusted R-squared: 0.8723 F-statistic: 39.05 on 7 and 32 DF, p-value: 6.52e-14 F-test There is strong evidence to indicate that at least one of the explanatory variables helps to predict a state’s poverty rate (p-value < 0.001, F-statistic(7, 32)=39.05). T-tests There is strong evidence to indicate that a state’s percentage of population being of color helps to predict a state’s poverty rate after accounting for the effects of its high school graduation 7 rate, median household income, percentage of households being food-insecure, cost of living index, natural environment quality, and healthcare quality (t-statistic32= 3.818, p-value < 0.001). There is not enough evidence to indicate that a state’s high school graduation rate helps to predict a state’s poverty rate after accounting for the effects of percentage of population being of color, median household income, percentage of households being food-insecure, cost of living index, natural environment quality, and healthcare quality (t-statistic32= -1.601, p-value = 0.119150). There is strong evidence to indicate that a state’s median household income helps to predict a state’s poverty rate after accounting for the effects of percentage of population being of color, high school graduation rate, percentage of households being food-insecure, cost of living index, natural environment quality, and healthcare quality (t-statistic32= -6.062, p-value < 0.001). There is some evidence to indicate that a state’s percentage of households being food-insecure helps to predict a state’s poverty rate after accounting for the effects of percentage of population being of color, high school graduation rate, median household income, cost of living index, natural environment quality, and healthcare quality (t-statistic32= 2.623, p-value = 0.013225). There is not enough evidence to indicate that a state’s cost of living index helps to predict a state’s poverty rate after accounting for the effects of percentage of population being of color, high school graduation rate, median household income, percentage of households being food-insecure, natural environment quality, and healthcare quality (t-statistic32= 1.100, p-value = 0.279581). 8 There is not enough evidence to indicate that a state’s natural environment quality helps to predict a state’s poverty rate after accounting for the effects of percentage of population being of color, high school graduation rate, median household income, percentage of households being food-insecure, cost of living index, and healthcare quality (t-statistic32= -0.706, p-value = 0.485478). There is not enough evidence to indicate that a state’s healthcare quality helps to predict a state’s poverty rate after accounting for the effects of percentage of population being of color, high school graduation rate, median household income, percentage of households being food-insecure, cost of living index, and natural environment quality (t-statistic32= 1.615, p-value = 0.116024). Least-Squares Regression Because several explanatory variables are found to be insignificant in the model (α = 0.05), I performed a backwards selection process to create a final model with significant predictors. Below is the least-squares regression equation from the final model: ︿ y = 14.78255161 + 0.11286699xpoc − 0.00023740xincome + 0.49433100xhunger + 0.06568734xhealthcare where… ︿ y = predicted poverty rate of a state (in %) xpoc = percentage of state population being of color (in %) xincome = state′s median household income (in $) xhunger = percentage of state′s households being f ood − insecure (in %) xhealthcare = state′s healthcare quality (in %) 9 Effects of Each Explanatory Variable For a state with a given median household income, percentage of food-insecure households, and healthcare quality, the poverty rate is predicted to increase by 0.11286699 for every additional percent increase in the percentage of a state’s population of color. For a state with a given percentage of population being of color, percentage of food-insecure households, and healthcare quality, the poverty rate is predicted to decrease by 0.00023740 for every additional dollar increase in a state’s median household income. For a state with a given percentage of population being of color, median household income, and healthcare quality, the poverty rate is predicted to increase by 0.49433100 for every additional percent increase in a state’s percentage of food-insecure households. For a state with a given percentage of population being of color, median household income, and percentage of food-insecure households, the poverty rate is predicted to increase by 0.06568734 for every additional percent increase in a state’s healthcare quality score. Conclusion With α = 0.05, there is strong evidence to indicate that at least one of the explanatory variables from our final model helps to predict a state’s poverty rate (p-value < 0.001, F-statistic(4, 35)=39.05). In addition, when accounting for the effects of the remaining explanatory variables, we found that each explanatory variable (percentage of population being of color, median household income, percentage of households being food-insecure, and healthcare quality) is a significant predictor in our final model. Therefore, to answer our question of interest... 10 “Does at least one of the following factors (percentage of population being of color, high school graduation rate, median household income, percentage of households being food-insecure, cost of living index, natural environment quality, and healthcare quality) have an effect on poverty rates in a state?” We can conclude that at least one of the explanatory variables in our final model have an effect on poverty rates in a state. From our final model, we can also conclude that the state’s percentage of population being of color, median household income, percentage of households being food-insecure, and healthcare quality can help predict the state’s poverty rate. From this point on, I believe that the U.S. needs to take a closer look at poverty’s possible influences and confounding factors. In this project, I did not account for such factors, which could change the final statistical model. Even so, this work gives a starting point for this needed research. For example, the percentage of the population being of color is a significant predictor of poverty. Why exactly is that, and how we can make progress in overcoming that? At a high level view, this project brings to light the many questions regarding our government, their current work, and their accountability to constituents. After all, America is seen as the pinnacle of freedom, liberty, and success, so as our government, it is fair for them to work even harder for our fellow constituents to be able to achieve the American Dream instead of the nightmare of poverty. 11 References Alston, P. (2018). Report of the special rapporteur on extreme poverty and human rights on his mission to the United States of America : note / by the Secretariat. United Nations. https://digitallibrary.un.org/record/1629536?ln=en Frederick, R. (2018, May 10). The environment that racism built. Center for American Progress. https://www.americanprogress.org/issues/race/news/2018/05/10/450703/environment-rac ism-built/ Newkirk II, V. R. (2018, February 28). Trump's EPA concludes environmental racism is real. The Atlantic. https://www.theatlantic.com/politics/archive/2018/02/the-trump-administration-finds-that -environmental-racism-is-real/554315/ United States Census Bureau. (n.d.). [Population statistics for all states and counties]. Retrieved June 7, 2020, from https://www.census.gov/quickfacts/fact/table/US/PST045219 U.S. News & World Report. (n.d.). Data Explorer [interactive graph on 2018 data]. Retrieved June 7, 2020, from https://www.usnews.com/news/best-states/data-explorer#{%22mode%22:%22column%2 2,%22year%22:2018,%22states%22:[],%22axes%22:{%22y%22:{%22key%22:%22ec_e mp_unem%22,%22type%22:%22value%22}}} state poverty poc graduation income col hunger environment healthcare Alabama 17.1 30.9 89.3 46257 87 17.7 40.6 24.6 Alaska 9.9 34.7 75.6 76440 122.4 13.9 40.7 48.6 Arizona 16.4 17.2 77.4 53558 98.9 15.8 41.6 53.9 Arkansas 17.2 20.9 84.9 44334 85.5 18.4 80.8 20 California 14.3 27.9 82 67739 128.3 12.5 31.6 68.4 Colorado 11 12.9 77.3 65685 99.1 12.2 78.1 70.8 Connecticut 9.8 20 87.2 73433 124.1 12.2 48.7 75.8 Delaware 11.7 30.5 85.6 61757 99.2 12.1 67.9 52.5 Florida 14.7 22.7 77.9 50860 95.7 15.1 83.9 42.1 Georgia 16 39.5 78.8 53559 90 16.2 72 30.4 Idaho 14.4 7 78.9 51807 86.4 14 63.6 62.1 Illinois 13 23.1 85.6 60960 100.5 11.7 22.9 50.2 Kansas 12.1 13.6 85.7 54935 90.3 13.2 70.3 48 Maine 12.5 5.4 87.5 53079 110.6 14.8 64.1 55.3 Maryland 9.7 41.2 87 78945 114.9 11.4 58.6 62.6 Massachusetts 10.4 19.2 87.3 75297 123.2 10.3 81.7 75.5 Michigan 15 20.7 79.8 52492 86.8 15.1 49 46 Mississippi 20.8 40.9 80.8 41754 81.9 21.5 77.5 3.2 Missouri 14 17 87.8 51746 88.1 15.6 72.7 37 Nebraska 11.4 11.7 88.9 56927 89.4 12.3 68.5 61.3 Nevada 13.8 25.7 71.3 55180 99.9 13.7 58.4 42.1 New Hampshire 7.3 6.8 88.1 70936 115.2 9.7 73.1 66.1 New Jersey 10.4 28 89.7 76126 113.8 10.8 51.2 67 New Mexico 19.8 18 68.6 46748 94.9 16 70.2 47.6 New York 14.7 30.3 79.2 62909 130.9 12.6 77 63.8 North Carolina 15.4 29.4 85.6 50584 90.2 16.5 48.4 37.8 North Dakota 10.7 13 86.6 60656 95.2 7.7 83.1 64.6 Ohio 14.6 18.1 80.7 52334 88.7 16 24.9 40.9 Oklahoma 16.3 25.8 82.5 49176 86.5 16.2 61.5 22.6 Oregon 13.3 13.2 73.8 57532 104.5 14.2 69 61.2 Pennsylvania 12.9 18.2 84.8 56907 100.5 13.1 30.5 54 Rhode Island 12.8 16.1 83.2 60596 114.8 12.5 80.9 71.4 South Carolina 15.3 31.5 80.3 49501 92.9 15.3 68.2 34.1 South Dakota 13.3 15.6 83.9 54467 95.3 12.1 80 57 Tennessee 15.8 21.5 87.9 48457 86.6 15.4 67.3 29.8 Texas 15.6 21.2 89 56565 91.4 15.7 44.1 37.5 Vermont 11.9 5.8 87.7 57677 112.7 11.9 63.2 71.9 Virginia 11 30.5 85.7 68114 98.1 11.2 43.4 48.4 Wisconsin 11.8 12.9 88.4 56811 93.4 11 69 62.1 Wyoming 11.3 7.4 79.3 59882 96 12.3 76.9 44.1
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