Multiple Linear Regression Proposal

Multiple Linear Regression Proposal

Abstract

In the study of science, Multiple Linear Regression is one of the most used statistical analysis. It is used to show the association between and a dependent and several predictors. In this paper, the crime index is the dependent variable while social status such as low, medium and high are the independent variables. The test hypothesis will show if there any significant association between the variables. The output will depict if there is any association when predictors are measured from with critical p-value of 0.05. From researches, it has been demonstrated that criminal activities have been associated with low social class level deducted from low income, low level of education, etc. Therefore, the hypothesis underlying will analyze any associations between crime and social status.

Multiple Linear Regression Proposal

During the research, when the association between two or more variables is needed, regression is the best aspect to consider. Multiple linear regression which is also known to be a multiple regression, is a statistical technique that uses several regressors to predict the outcome of a response variable (Nathans et al., 2012). The response variable is denoted by “Y” while the explanatory variables are indicated by “Xis”. The purpose of multiple linear regression is to model the direct relationship between independent variables and the response, which is the dependent variable. Multiple linear regression is an extension of a simple linear regression which involves one predictor variable (Nathans et al., 2012). From the posted weekly question asked: Is there any relationship between crime and social class? Hence in this work, I will use Multiple Linear Regression (MLR) analysis to explore how various variables of social class which include low, medium and high level negatively or positively affect crime. Despite having different types of regression analysis such as logistic, logit or simple linear regression, this type is useful in this study since the observations are selected independently and randomly from the population.

When using Multiple Regression, we reduce the confounding of variables so that we eliminate the bias of coefficient estimates. The p-value of the coefficient is used to determine if there is an association between the predictors and the response and conclude if to accept or reject the hypothesis. In the question given to test if there any association between social class and crime, we shall use the levels of social status and determine which level contribute much to someone committing a crime using their coefficients.

When finding the relationship between the variables using Multiple Linear Regression, the following null and alternative hypothesis are formulated;

The null hypotheses posed from the question is that there is a significant association between someone committing a crime and social class status such as high, low or medium.

The alternative hypothesis is that crime done by individuals does not depend on the social status of the people; hence no significant association between the predictors and the response. From the study, we shall consider everybody because no matter the social class, everyone can be involved in criminal activities

Methods of data collection

The population to be considered in this research will include twenty (20) middle-aged males’ inmates of different social status such as low, medium and high. The inmates will be of specifically of the age group of 24-29 years, and the data will be collected from the same area where they did the crime. The data will be obtained from the records of police and study of their prior life history and that of their family including their mode of income, level of education and if their family have a tendency of criminal records so that we can see if those characteristics lead them to be involved in criminal activities.

Procedures

This research will involve crime index and social status of the inmates as the main variables to be used in the analysis and developing the multiple linear regression. The social status will be used to gauge the index to which the individual commits the crime. The crime index is a ratio scale as it can go from actual zero to a maximum index (Troy, et al., 2012). The crime index is a discrete scale of measurement because you can count the number of crimes the individual involved, and you can see which crime is mostly committed. The crime index is a quantitative variable as you can count the number of crime an individual commits.

Social status is an ordinal variable as in involves an ordered relationship between some sub-variables(Fattore et al., 2012)., i.e. low, medium and high this because when an individual has committed five types of crime and another one ten types of we can order them accordingly. Social status is a continuous variable as it involves people from different social class, but despite being in the same quality, they don’t have the same characteristics. A status variable is qualitative as it depicts what class an in-mate come from when considering his background, level of education or his family characteristics. These descriptions are useful since they can be used for further study by researchers; therefore, they are of validity and should be followed carefully.

Despite social status being a qualitative variable, its measurements such as low, medium and high will be used to predict the crime index. The rate of crime by the inmates will be measured quantitatively and will give the values to be used as “Y” values.

Results

In this research, Multiple Linear regression will be of use as it will show the association or the effect that social status has on the crime rate. From a general view of things, low social status will result in high criminal activities since they have low income, they have low-level education than those who came from a high social level. In other views, some people who came from social classes still engage in criminal activities since they got resources to do the crime, and they want more of them to maintain the social level. Therefore, to avoid biases, Multiple Regression will be used to show the actual effect of these measures.

The results depicted will provide a conclusion on whether to reject or accept the null hypothesis. Furthermore, to get the actual association, we shall use the P-value of the determinants and compare them with 5% level of significance, and if they are greater than the critical value, we shall reject the null hypothesis( Zhang et al.,  2013).

Bias in the study will result if an inmate is indicated to come from a social class different from where he comes. The model will be based on the following assumptions; a linear association between the predictors and response, predictors are not highly correlated among them, the response will be independently and randomly selected from the population, and residual are distributed with mean zero and variance sigma (σ) (Winter, 2013).

The following conclusion will be drawn concerning which level of social status will affect or associate more with the crime index in the city, keeping in mind that the level of significance must be met. This research is essential to the police as they can use it to know which class is mostly engaged in criminal activities so that they can formulate procedures on how to combat them.

Fattore, M., Maggino, F., & Colombo, E. (2012). From composite indicators to partial orders: evaluating socio-economic phenomena through ordinal data. In Quality of life in Italy (pp. 41-68). Springer, Dordrecht.

Nathans, L. L., Oswald, F. L., & Nimon, K. (2012). Interpreting multiple linear regression: A guidebook of variable importance. Practical Assessment, Research, and Evaluation, 17(1), 9.

Troy, A., Grove, J. M., & O’Neil-Dunne, J. (2012). The relationship between tree canopy and crime rates across an urban–rural gradient in the greater Baltimore region. Landscape and urban planning, 106(3), 262-270.

Winter, B. (2013). Linear models and linear mixed effects models in R with linguistic applications. arXiv preprint arXiv:1308.5499.

Zhang, S., Chen, H. S., & Pfeiffer, R. M. (2013). A combined p-value test for multiple hypothesis testing. Journal of Statistical Planning and Inference, 143(4), 764-770.