Relationship between Poverty, Family Size, and Other Variables - Statistics Project Example

Introduction Poverty rate in recent years has increase due to lack of job opportunity, high family size with low income. This variable depicts an inverse relationship between the poverty rate and this variable. In this regard, a government should balance between the family size, level of income and unemployment in order to ensure that there is a decline in poverty rate. Some of the model employed in ascertaining the relation and significance of the variables and the poverty rate is as follows. The model is assumed at 95% confidence level and thus we are certain that the result generated by the model will be relied upon in making a decision since, the standard error will depict the small portion of unexplained variables by the model. These unexplained variables are factors beyond the control of the model such as the external factors. Relationship between poverty and Income From the above data analysis, we are confident that at 95% confidence level, the poverty mean is 9.17 with a variance and standard deviation of 7.1928 and 2.6819 respectively. The histogram depict that an increase in the level of income would lead to a decline in the poverty rate. In this regard, income is a major determinant of poverty rate hence, to eradicate poverty; the individual income level should as well as increase (Alemayehu Bishaw 2008). We are therefore certain that at 5% significance level, the result generated by the model can be fully relied upon since, the model depict a small standard error from the deviation. The small standard error is due to other external factors that affect the model since, as per the variable analysis, they are unexplained by the model. Relationship between poverty and family size The family size proves an average mean of 9.028 with a standard deviation and variance of 2.4157 and 5.8356 respectively. IT therefore implies that, as the family size increase, the poverty level increases as well. The government ought to ensure that there is ideal family size that the government can provide the right service perfectly and thus, the poverty rate will reduce due to the fact. There is high disposable income from the managed family size. The high disposable income would lead to increase in per capita income and thus the poverty rate will reduce. In this regard, the above graph analysis can be relied upon in assessing the extent to which the family size increase or decrease the poverty rate since, an inverse relationship between the variable is eminent. Relationship between poverty and urban The above data analysis provides that, an increase in the level of urban would lead to a decline in poverty rate with a mean of 9.028 and a standard deviation of 2.4157.This consequently implies that, development of urban centre reduces poverty due to increase in the level of income with enhanced economy. In summary the above four variables have a positive correlation between poverty and living standard (Estonian investment Agency 2014). It is apparent that an increase in family size would lead to an increase in poverty level since, per capita income of individual will be minimal, and the increase in the level of income would lead to a reduction poverty rate due to improved living standard of individual. In order to minimize poverty rate, the government should therefore ensures that there is increase urban growth together with enhanced income and a reduction in family size as depicted form the above graph analysis. The median household income was used since; there is always a strong positive correlation between the poverty rate and the level of income. The higher the income level, the lower the poverty rate and thus this is a good approach to ascertain the poverty rate as far as the level of income is concerned. The histogram above provides that, where there is an increase in the level of income, a reduction in poverty rate is envisaged and thus it implies that, in order to eradicate poverty rate, individual ought to be provided with job opportunity that will increase their per capital income as well as boost their living standard. Correlation co-efficient between Poverty and other variable Equation Parameters 68.66% of the change in County can be explained by the change in the 4 independent variables 95% Confidence/Autocorrelation R Squared 0.7141 0.439 Durbin-Watson Statistic Adjusted R Squared 0.6866 1.41 - 1.72 Positive autocorrelation detected Standard Error 9.4532 to +/- on result of Regression Equation 2.377 Critical F-Statistic - 95% Confidence F - Statistic 25.9789 Therefore analysis IS Significant 89.60% Confidence to which analysis holds Multiple Regression Equation   Coefficients Standard Error t Stat p Value Intercept 45.246 3.388 13.355 0.00% POV 0.036 0.041 0.878 38.42% INCOME -0.839 0.214 -3.910 0.03% FAMILY SIZE -18.406 4.610 -3.992 0.02% URB -3.313 3.579 -0.926 35.89% The above data analysis depicts a correlation co-efficient between POV and other variables. It can be concluded that there is a small co-efficient of variation between poverty and other variable contributing to poverty rate implying that the variables can be relied upon in making an analysis concerning the increase in poverty rate and its effect. The variable depict a small standard error hence, the information can be relied upon in concluding on the information provided by the histogram due to small standard error combined with small coefficient. This information generated by the model is at 5% significance level implying that there is low standard error of estimates and has a result, the external factors that might affect the reliability of the figure is minimal (Kolb 2011). Nevertheless, the analyst should not disregard the external factors affecting the result generated since, these factors contribute significantly to the result of the model hence, in making a rightful as well as reliable conclusion, and both internal and internal factors affecting the result must be incorporated. Regression equation POVi =α + β1FAMSIZEi + β2URBANi +β3URi + β4INCOMEi + ui Where the i subscript corresponds to Californian county i. Interpret the coefficients estimates and comment on their statistical significance. Equation Parameters 68.66% of the change in poverty can be explained by the change in the 4 independent variables R Squared 0.7141 Adjusted R Squared 0.6866 Standard Error 9.4532 to +/- on result of Regression Equation F - Statistic 25.9789 Therefore analysis IS Significant Interpreting the equation parameters The equation implies therefore, 69% of the change in poverty rate can be explained by change in the four variables, while 31% of the variables are unexplained by the model. The statistical significance of the variable therefore implies that the information cannot be fully relied upon since; other factors (31% unexplained) affect the result of the analysis. In this regard, the external factor that would affect the analysis ought to incorporate in the equation parameters in order to; minimize the 31% of the unexplained variables. The model can therefore be relied upon in making decision since; the model is significant due to low standard error accompanied with 95% confidence level that 69% of the variables will be explained by the model. Interpreting R squared Independent Analysis Auto Correlation Multicollinearity R Squared Coefficient Intercept Dl=1.53 Du=1.60 Adjusted R-Squared against other Index Variables With RSQ at > 90%       DW-Stat 5.26% 0.12 22.35 2.12 0.99%   51.73% -1.53 39.06 0.55 41.65%   55.68% -25.21 47.17 0.22 68.25%   22.84% -19.18 33.80 2.14 25.61%               Interpreting the R2 statistic and test if it is statistically significant R squared also known as the coefficient of determination is a statistical tool for measuring how close the data are to the fitted regression line. Therefore, the above data analysis, the model depict an average (55%) variability of the data around the mean. In this regard, the model do not fully explains the variability and consequently other external factors that affect the model need to be considered in order to guarantee for 100 % variability of the R square and the model to be considered significant. In this regard, the test statistic is not significant since, the model do not fully explains the variability hence, the verdict generated by the model cannot be fully relied upon due to high standard error accompanied with high variance from the return (Ooghe 2000). The test statistics ought to be close 95% variability in order to be statistically significant and be relied upon in making an investment decision concerning the poverty rate and other variable affecting it. Poverty rate at an unemployment rate of 12% Equation Parameters 80.66% of the change in poverty can be explained by the change in the 4 independent variables R Squared 0.9241 Adjusted R Squared 0.8066 Standard Error 10.6532 to +/- on result of Regression Equation F - Statistic 26.1789 Therefore analysis IS Significant An increase in unemployment rate by 12% would lead to an increase in poverty rate by 12% consequently. This is depicted by increase in value of the standard error of 10.64.In this regard, 80.66% of the variable will be explained by the model while 19.34% is unexplained. In this regard, the model is considered significant due to the fact that there is high value of coefficient of determination as well as that of F-test (26.179).As a result, the model expound that an increase in the level of unemployment would lead to an increase in poverty rate and as a result, an inverse relation is depicted. Changes to the result An increase in unemployment rate would lead to increase in poverty rate. The above data analysis depict a coefficient of multiple determination of 80.66%, with F-test of 26.178 and a standard error of 10.65.In this regard, the values can graphically be explained as close to the line of best fit in which case it poof that the model is significant that is, much of the variable is explained by the model and the analysis is significant. In this regard, a positive correlation exist between unemployment rate and poverty since, the per capita income of individual is low leading to poor living standard and consequently in crease inn poverty and crime rate (Reynolds Farley 2000). To get rid of this situation, the government should ensure that there is reduction of unemployment rate. This can be achieved through creating more job opportunity, managing the birthrate as well as ensuring that the citizen gets the right education. Conclusion There is always a positive correlation between poverty and the variable explained above, this has been explained by the model .The R squared aloes known as coefficient of multiple determination tries to explain how close the data to the line of best fit is. The close the data to the line of best fit, the more the model explains the variability of the data and thus the analysis is significant. At 95% confidence level about the mean, we are certain that the information and data provided can be relied upon for decision making and thus the above data analysis provide the variables and its effect on poverty at 95% confidence level to be at a mean of on average with a standard deviation 2.5% on average (Webster 2010). In this regard, it can therefore be concluded that an inverse relationship exist between the poverty rate and the four variables (income level, urban growth, family size and unemployment rate. The county executives should strive to ensure that the above four valuable is kept at an ideal level that would minimize the poverty rate and increase in the living standard of individual as explained by the regression and correlation model. Other external factors that affect the result of the model must as well be considered in concluding on the final result generated by the model in guaranteeing on the poverty rate at present. This because, the unexplained variable as much as it depict a small portion, contribute as well as to increase in poverty rate, Net effect of this is that, the result generated can be fully relied upon in making decision on the approach to minimize the poverty rate within the shortest time possible as well as ensuring that there is stable economic growth in the county. Bibliography -, JS 2011, The End of Poverty: How We Can Make it Happen in Our Lif. Alemayehu Bishaw, ‎S 2008, Income, Earnings, and Poverty Data From The 2007 American. Estonian investment Agency 2014, 'Financing a business', wall street. Kolb, RW 2011, Financial Contagion: The Viral Threat to the Wealth of Nations. Ooghe, H 2000, The Economic and Business Consequences of the EMU. Reynolds Farley, ‎H 2000, The American People:. Webster, BH 2010, Income, Earnings, and Poverty Data from the 2005 American. Read More