In this project we consider a time series data to analyze the whether the effect of capital punishment on homicide rate. Time series analysis is a form of statistical data analysis on a series of sequential data points that are usually measured at uniform time intervals over a period of time. A time series can be said to collection of data with the interval between and being fixed and constant. Time series analysis is the estimation of difference equations containing stochastic (error) terms (Enders 2010).

Time series forecasting takes the analysis from the time series data and tries to predict what the data may be in the near future, based on what it has been in the past. But because there are many factors influencing the fluctuation of the homicide, creating an accurate forecast based on the analysis alone is difficult. Therefore, many approaches and models have to be developed in order to utilize the time series analysis and provide an accurate prediction of what is to come in the future. The purpose of this report is to apply the statistical techniques to understand the relationship, if any exists, between capital punishment and homicide rate.

There is a strong correlation between the homicide rate and death penalty number (number under capital punishment); from the table generated below on the correlations, the correlation coefficient = 0.9406* implying a strong positive correlation between the homicide rate and death penalty number.

To explain the concept of the correlation further, a scatter plot representing the homicide rate and number of people under death penalty in a given year is plotted and from the pattern of the graph, it can easily be seen that there is a strong positive correlation/relationship between homicide rate and number of people under death penalty. For instance, for any unit increase in homicide rate there is a subsequent increase in the number of people under death penalty likewise for any unit
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