| STATE PUBLIC EXPENDITURES |
| By |
| THE PLACEBOS |
| Marie Gerke |
| Vickie Tobiassen |
| Natalya Sviridyuk |
| Diana Welters |
| March 17, 2004 |
| ����������� Our project explored statistical data based on state public expenditures.� We chose four different variables to analyze; they are:� Local public expenditures per state capita (EX), economic ability index (ECAB), percentage of the population that is living in metropolitan areas (MET), and the percentage change in population between 1950 and 1960(GROW).� State names were used as classification. |
| EX - Local Public Expenditures per State Caapita |
| The EDA has pointed out one definite, Wyoming (454), outlier and one suspected outlier, Nevada (421).� The mean and median are essentially equal.� We are ninety-five percent confident that the mean is between 271.99 and 305.05.� We are also ninety-nine percent confident that the mean is between 266.81 and 310.23. |
| Minimum |
| 183 |
| Q1 |
| 256 |
| Median |
| 288.5 |
| Q3 |
| 325 |
| Maximum |
| 454 |
| 1.5 IRQ of Q3 |
| 428.5 |
| Outliers |
| 454 |
| % Outliers |
| 2.0833% |
| 1.5 IRQ of Q1 |
| 152.5 |
| Outliers |
| 0 |
| % Outliers |
| 0.0000% |
| M + 2S |
| 405.36 |
| Outliers |
| 421 & 454 |
| % Outliers |
| 4.1667% |
| M - 2S |
| 171.68 |
| Outliers |
| 0 |
| % Outliers |
| 0.0000% |
| S^2 (Variance) |
| 3412.47 |
| Mean |
| 288.52 |
| 95% C.I. |
| 271.99 |
| To |
| 305.05 |
| 99% C.I. |
| 266.81 |
| To |
| 310.23 |
 |
| This box plot might look a little skewed because of the layout and position of the outlier, Wyoming.� The distribution is normal because the difference between the mean and median is minimal. |
 |
| The following is a linear regression of the local public expenditures per state capita.� Wyoming and Nevada's plots are the two points on the far right, while South Carolina is the lowest point.� As you can see, there is a Strong Positive Correlation (0.996617) between the data and the linear regression.� |
 |
| ECAB - Economic Ability Index |
| The Economic Ability Index is composed of income; retail sales; and the value of output of manufacturing, minerals, and agricultural per capita.� The EDA shows us that Nevada is a definite outlier with an economic ability index of 205.� Mississippi has the lowest economic output at 57.4.� The mean is slightly more than the median.� We are ninety-five percent confident that the mean is between 90.46 and 103.04.� We are also ninety-nine percent confident that he mean for the Economic ability index is between 88.48 and 105.02. |
| Minimum |
| 57.4 |
| Q1 |
| 85.3 |
| Median |
| 95.3 |
| Q3 |
| 105.9 |
| Maximum |
| 205 |
| 1.5 IRQ of Q3 |
| 136.8 |
| Outliers |
| 205.0 |
| % Outliers |
| 2.0833% |
| 1.5 IRQ of Q1 |
| 54.4 |
| Outliers |
| 0 |
| % Outliers |
| 0.0000% |
| S (St. Dev) |
| 22.25 |
| M + 2S |
| 141.25 |
| Outliers |
| 205.0 |
| % Outliers |
| 2.0833% |
| M - 2S |
| 52.25 |
| Outliers |
| 0 |
| % Outliers |
| 0.0000% |
| S^2 (Variance) |
| 495.2 |
| Mean |
| 96.75 |
| 95% C.I. |
| 90.46 |
| To |
| 103.04 |
| 99% C.I. |
| 88.48 |
| To |
| 105.02 |
 |
| The box plot shows a slight skewness to the left.� Nevada is the outlier to the far right.� |
 |
| The following is a linear regression of the Economic Ability Index.� Mississippi is the first data plot, while Nevada is the last data point.� This data also has a Strong Positive Correlation (0.8400). |
 |
| MET - Metropolitan Population |
| This variable is symmetric.� There are no outliers in this data, but there are three states with 0.00 percentage of their population in metropolitan areas.� They are Vermont, Idaho and Wyoming.� California has the highest percentage of 86.5, while Rhode Island follows closely with 86.2%.� New York comes in third with 85.5%.� The mean and median are essentially equal. |
| Minimum |
| 0 |
| Q1 |
| 23.6 |
| Median |
| 46.15 |
| Q3 |
| 70.45 |
| Maximum |
| 86.5 |
| 1.5 IRQ of Q3 |
| 140.73 |
| Outliers |
| 0 |
| % Outliers |
| 0.0000% |
| 1.5 IRQ of Q1 |
| -46.68 |
| Outliers |
| 0 |
| % Outliers |
| 0.0000% |
| S (St. Dev) |
| 26.94 |
| M + 2S |
| 100.05 |
| Outliers |
| 0 |
| % Outliers |
| 0.0000% |
| M - 2S |
| -7.71 |
| Outliers |
| 0 |
| % Outliers |
| 0.0000% |
| S^2 (Variance) |
| 725.7 |
| Mean |
| 46.17 |
| 95% C.I. |
| 38.55 |
| To |
| 53.79 |
| 99% C.I. |
| 36.16 |
| To |
| 56.18 |
 |
| This box plot show, that the distribution is uniform because the whiskers are the same length as the boxes. |
 |
| This linear regression shows a strong positive correlation (0.995968) with the data.� The states of Vermont, Idaho and Wyoming are represented by the one data plot at (0,-2).� California, Rhode Island and New York are the three data points above the regression line, on the right side. |
 |
| GROW - Percentage of Growth in the Population from 1950 - 1960 |
| This is a mound shaped distribution with three definite outliers of Nevada, Florida and Arizona.� They grew by 77.8%, 77.2% and 74.3%, respectively.� Two states had negative growth.� They are West Virginia with -7.4% and Arkansas with -6.2%.� In this variable the mean is noticeable larger than the median. |
| Minimum |
| -7.4 |
| Q1 |
| 6.95 |
| Median |
| 14.05 |
| Q3 |
| 23.15 |
| Maximum |
| 77.8 |
| 1.5 IRQ of Q3 |
| 47.45 |
| Outliers |
| 74.3, 77.2, & 77.8 |
| % Outliers |
| 6.2500% |
| 1.5 IRQ of Q1 |
| -17.35 |
| Outliers |
| 0 |
| % Outliers |
| 0.0000% |
| S (St. Dev) |
| 18.87 |
| M + 2S |
| 56.47 |
| Outliers |
| 74.3, 77.2, & 77.8 |
| % Outliers |
| 6.2500% |
| M - 2S |
| -19.01 |
| Outliers |
| 0 |
| % Outliers |
| 0.0000% |
| S^2 (Variance) |
| 356.26 |
| Mean |
| 18.73 |
| 95% C.I. |
| 13.39 |
| To |
| 24.07 |
| 99% C.I. |
| 11.72 |
| To |
| 25.74 |
 |
| This distribution is not-normal because the whiskers and boxes on the right side are longer than the left side.� The outliers of Nevada, Florida and Arizona are to the extreme right of this box-plot. |
 |
| The linear regression shows the three outliers of Nevada, Florida and Arizona, with the most growth and the two states, West Virginia and Arkansas with negative growth.� This regression shows a strong positive correlation (0.855214) of the data. |
 |
| CORRELATION MATRIX AND PREDICTED VALUES |
| The correlation matrix shows the different correlations between the variables.� These correlations are all moderate positive correlations.� The strongest correlation is between the local public expenditures per state capita and the economic ability index. |
| EX |
| ECAB |
| MET |
| ECAB |
| 0.655863 |
| MET |
| 0.045235 |
| 0.408926 |
| GROW |
| 0.045235 |
| 0.460072 |
| 0.404023334 |
| Predicted Y values |
| Correlation formula: |
| Y = 0.2294X + 30.571 |
| X = EX |
| Y = ECAB |
| X = 198 |
| 75.992 |
| X = 321 |
| 104.208 |
| X = 369 |
| 115.22 |
 |
 |
 |
| Varying public expenditures per capita among states are mainly determined by economic ability.� Nevertheless, two factors can and do modify the relationship of economic ability and expenditures.� The first factor is Nevada, which has an economic ability index value of 205.0 greater than that of any other state.� Therefore, it influences the overall regression.� The second factor is that the western states exceed eastern states in per capita expenditures. |
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