Regression Analysis: Causal Relationships and Model Assumptions

This discussion post focuses on regression analysis, a statistical method used to test causal hypotheses in social science research. The author, along with a response from another student, explores real-world examples, such as Air Force recruitment, where regression analysis helps predict outcomes and identify influencing factors. The post highlights how regression analysis can be used to create a better way to conduct business, especially in sales. The discussion includes the importance of understanding the dependent and independent variables. The response also emphasizes the critical assumptions necessary for valid regression modeling, including linear relationships, multivariate normality, no multicollinearity, no autocorrelation, and homoscedasticity. These assumptions ensure the reliability and accuracy of the regression model's results, whether it's simple linear regression, multiple linear regression, polynomial regression, ridge regression, or lasso regression.

Module 4 Discussion
Roberto Hernandez posted May 2, 2017 12:46 AM
 Dr. Liu and classmates,
Taylor (2010), states that regressions are form of statistical analysis frequently used to
test casual hypothesis in social science research. Two examples of situations where
regression was used as an Air Force Recruiter. The first situation was determining that
young adults graduating from high school would visit the recruiting office after
graduation. The factor was that recent graduates were not ready to go to college, but
wanted to become independent and would join the Air Force. Every year as a recruiter the
number of recent graduates that would come to the recruiting office were higher than
those that had graduated years earlier. Another situation was the number of special forces
applicants would increase when there was an invitation to take the physical test at the
local gym. The test was conducted by active duty special forces members and it was
advertised to everyone in the schools, local community, and media outlets. The number
of applicants rose compared to not having any special event. Regression analysis is useful
in applications because it helps when predicting an outcome and identifying the
impacting factors. This helps to create a better way to conduct business, especially in
sales.
Robert
References:
Taylor, M.Z.. (2010). 21st Century Political Science: A reference handbook. Chapter 57
Regression Analysis. Georgia Institution of Technology. Retrieved 2010. From:
http://web.a.ebscohost.com.ezproxy.trident.edu:2048/ehost/ebookviewer/ebook/
ZTAwMHhuYV9fNDgxMTAxX19BTg2?sid=4d2673ab-9a37-46bf-b4c5-
8db602d16b63@sessionmgr4006&vid=0&format=EB&rid=1
You are correct about the use of regression modeling to test the causal relationships but there are few
assumptions are needed to run regression which are necessary to check before modeling process. These
are the assumptions which enables us to make use regression efficiently for better results, lets list them
and discuss a little bit as below:
1. Linear Relationship: The dependent variable and independent variable must be linearly related to
each other.
2. Multivariate Normality: All the variables included in the model should be normally distributed.
3. No Multicollinearity: All the independent variables must be independent from each other.
4. No Autocorrelation: The residuals should be independent from each other.
5. Homoscedasticity: The variance of all variables must have same finite variance.

These are the basic assumptions that are checked, whether we perform simple linear regression,
multiple linear regression, polynomial regression, ridge regression, or lasso regression.
Now coming on the examples, you have provided, I would suggest to explain the dependent variable,
and independent variable(s) in a way that it would easier to relate how these are related to each other.
For example: the factor explained that recent graduates were not ready to go to college but wanted to
become independent by joining Air Force, so how this data can be collected and display a causal
relationship scenario would be a better way to explain the use of regression for testing causal
relationship.