Stats Project - Regression Analysis
STA9708
Regression Analysis: Literacy rates and Poverty rates
As we are aware, poverty rate serve as an indicator for a number of causes in the world. Poverty rates are linked with infant mortality, education, child labor and crime etc. In this project, I will apply the regression analysis learned in the Statistics course to study the relationship between literacy rates and poverty rates among different states in USA. In my study, the poverty rates will be the independent variable (x) and literacy rates will be the dependent variable (y). The purpose of this regression is to determine if there is a correlation between the poverty rates and literacy rates in different states within USA. My null and alternate hypothesis are as follows:
Null hypothesis: Ho: β1 = 0 This hypothesis states that there is no correlation between the literacy and poverty rates
Alternate hypothesis: Ha: β1≠0 This is the hypothesis we want to prove, there is correlation between the literacy rate and poverty rates
The first step I did was to create a scatter plot for the data and the descriptive statistics study. The scatter plot shows a positive correlation between the two variables and the equation of the line is y = 1.0998x + 2.2613 with a R-square value of 0.5305. The scatter plot is shown below:
Figure 1: Scatter plot of relationship between poverty and literacy rates
Based on the coefficient of determination of 0.53, we can say that poverty rate is contributing about more than half to the increase in literacy rates in states. The Y-intercept represents the literacy rate without any poverty rate contribution to the states.
After the scatter plot, I calculated the descriptive statistics of the dependent variable (y) which is the Literacy rates. The mean literacy rate is 14.76 and the standard error is 1.01. Shown below is the result from the descriptive statistics: Literacy rates - descriptive stats | | | Mean | 14.76036172 | Standard Error | 1.002134285 | Median |
Regression Analysis: Literacy rates and Poverty rates
As we are aware, poverty rate serve as an indicator for a number of causes in the world. Poverty rates are linked with infant mortality, education, child labor and crime etc. In this project, I will apply the regression analysis learned in the Statistics course to study the relationship between literacy rates and poverty rates among different states in USA. In my study, the poverty rates will be the independent variable (x) and literacy rates will be the dependent variable (y). The purpose of this regression is to determine if there is a correlation between the poverty rates and literacy rates in different states within USA. My null and alternate hypothesis are as follows:
Null hypothesis: Ho: β1 = 0 This hypothesis states that there is no correlation between the literacy and poverty rates
Alternate hypothesis: Ha: β1≠0 This is the hypothesis we want to prove, there is correlation between the literacy rate and poverty rates
The first step I did was to create a scatter plot for the data and the descriptive statistics study. The scatter plot shows a positive correlation between the two variables and the equation of the line is y = 1.0998x + 2.2613 with a R-square value of 0.5305. The scatter plot is shown below:
Figure 1: Scatter plot of relationship between poverty and literacy rates
Based on the coefficient of determination of 0.53, we can say that poverty rate is contributing about more than half to the increase in literacy rates in states. The Y-intercept represents the literacy rate without any poverty rate contribution to the states.
After the scatter plot, I calculated the descriptive statistics of the dependent variable (y) which is the Literacy rates. The mean literacy rate is 14.76 and the standard error is 1.01. Shown below is the result from the descriptive statistics: Literacy rates - descriptive stats | | | Mean | 14.76036172 | Standard Error | 1.002134285 | Median |
References: 1. Chapter 12 class notes 2. http://nces.ed.gov/naal/estimates/StateEstimates.aspx 3. http://www.cepr.net/documents/publications/Congressional_Districts/state_poverty_rates.pdf