Multivariate Logistic Regression Analysis

Introduction

Hypothesis testing is a necessary step in every statistics exercise to predict the outcome of a certain treatment component as might be desired by the researcher. In statistic treatment, several different methods may be applied to predict the outcome of an experiment or research under the interest of the involved researcher. Those methods apply to the different aims of the researcher in carrying them out and yield different results that would require interpretations to make sense in the project being undertaken. Their usefulness is however tied to the accuracy and skill yielded by the involved individuals in designing, carrying out, analysis and interpretation of the data collected for the research. Logistic regression analysis is one such method comprising of simple and multiple methods. Multiple logistic regression analysis involves a single dichotomous outcome to be arrived at using several independent variables while simple logistic regression analysis involves a single independent variable. In this exercise, the researcher looked at the treatment of a sample involving a single dichotomous outcome arising from several independent variables ascertain their standing on the developed hypothesis. The results were then analyzed and presented in the paper.

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The main aim of the exercise was to determine the attitudes that influenced the voting patterns among members of the population. In conducting the exercise, several attitudinal variables that might have led to the voting in of President Trump. Treatment of the variables allowed the researcher to develop a hypothesis subject to testing, which included the following:

• Null hypothesis: Employment was not the main attitude variable that influenced the voting in of Trump among the population.
• Alternate hypothesis: Employment was the main attitude variable that influenced the voting in of Trump among the population.

The results from the multivariate logistic regression test give us the results presented in the table below.

Using the equation . , where is the expected probability that the outcome is present; X1 through Xp are distinct independent variables, and b0 through bp are the regression coefficients, we analyze the results according to our main aim, looking at the most significant variable that impacted Trump's election.

Looking at the data from the table, we can focus on the variables which are employed. In regards to the prediction of Trump votes, we can quickly eliminate religion as a significant variable since they mostly composed of a large p-value. There is also a huge disparity among the different religions that make it difficult to use as an accurate predictor. Race portrays a lower range of disparity with them, and thus its significance diminishes as an accurate predictor. Employment and income levels are also significant predictors as their p-values are significantly low at 0.00069 and 0.000413 respectively. However, employment has a large effect size regarding log odds and log odds ratios. This would make it an ideal candidate as the most significant predictor of trumps win.

Conclusion

Having come up with the above conclusion from our analysis, we could then go back to our hypothesis in this case and evaluate them according to our findings. Given the evidence of a great impact and significance of employment as a predictor of Trump's votes, we could thus reject the null and accept our alternate hypothesis that "Employment was the main attitude variable that influenced the voting in of Trump among the population."