MATH 225N Week 8 Discussion: Correlation and Regression

Chamberlain University MATH 225N Week 8 Discussion: Correlation and Regression– Step-By-Step Guide

This guide will demonstrate how to complete the Chamberlain University MATH 225N Week 8 Discussion: Correlation and Regression   assignment based on general principles of academic writing. Here, we will show you the A, B, Cs of completing an academic paper, irrespective of the instructions. After guiding you through what to do, the guide will leave one or two sample essays at the end to highlight the various sections discussed below.

How to Research and Prepare for MATH 225N Week 8 Discussion: Correlation and Regression              

Whether one passes or fails an academic assignment such as the Chamberlain University MATH 225N Week 8 Discussion: Correlation and Regression  depends on the preparation done beforehand. The first thing to do once you receive an assignment is to quickly skim through the requirements. Once that is done, start going through the instructions one by one to clearly understand what the instructor wants. The most important thing here is to understand the required format—whether it is APA, MLA, Chicago, etc.

After understanding the requirements of the paper, the next phase is to gather relevant materials. The first place to start the research process is the weekly resources. Go through the resources provided in the instructions to determine which ones fit the assignment. After reviewing the provided resources, use the university library to search for additional resources. After gathering sufficient and necessary resources, you are now ready to start drafting your paper.

How to Write the Introduction for MATH 225N Week 8 Discussion: Correlation and Regression              

The introduction for the Chamberlain University MATH 225N Week 8 Discussion: Correlation and Regression  is where you tell the instructor what your paper will encompass. In three to four statements, highlight the important points that will form the basis of your paper. Here, you can include statistics to show the importance of the topic you will be discussing. At the end of the introduction, write a clear purpose statement outlining what exactly will be contained in the paper. This statement will start with “The purpose of this paper…” and then proceed to outline the various sections of the instructions.

How to Write the Body for MATH 225N Week 8 Discussion: Correlation and Regression              

After the introduction, move into the main part of the MATH 225N Week 8 Discussion: Correlation and Regression assignment, which is the body. Given that the paper you will be writing is not experimental, the way you organize the headings and subheadings of your paper is critically important. In some cases, you might have to use more subheadings to properly organize the assignment. The organization will depend on the rubric provided. Carefully examine the rubric, as it will contain all the detailed requirements of the assignment. Sometimes, the rubric will have information that the normal instructions lack.

Another important factor to consider at this point is how to do citations. In-text citations are fundamental as they support the arguments and points you make in the paper. At this point, the resources gathered at the beginning will come in handy. Integrating the ideas of the authors with your own will ensure that you produce a comprehensive paper. Also, follow the given citation format. In most cases, APA 7 is the preferred format for nursing assignments.

How to Write the Conclusion for MATH 225N Week 8 Discussion: Correlation and Regression              

After completing the main sections, write the conclusion of your paper. The conclusion is a summary of the main points you made in your paper. However, you need to rewrite the points and not simply copy and paste them. By restating the points from each subheading, you will provide a nuanced overview of the assignment to the reader.

How to Format the References List for MATH 225N Week 8 Discussion: Correlation and Regression              

The very last part of your paper involves listing the sources used in your paper. These sources should be listed in alphabetical order and double-spaced. Additionally, use a hanging indent for each source that appears in this list. Lastly, only the sources cited within the body of the paper should appear here.

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Sample Answer for MATH 225N Week 8 Discussion: Correlation and Regression

Regression analysis is how we measure cause and affect relationships and determine if they are statistically sound or not. Correlation alone is not causation and that is why patterns and influence must be studied (Holmes, Illowsky, and Dean, 2017). If a regression analysis were done on BMI, there are many probable independent variables. The easiest one and most common to think of would be the patient’s diet. We could break this down and become more specific such as total cholesterol intact or total fat intact. Other variable to consider would be exercises or illnesses such as lipedema or lymphedema. Also, things such as COPD and CHF are important to consider. As mentioned in our lesson this week, correlation is not causation and conducting further experiments and statistics is needed to determine whether the results are based on influence or coincidence.

In a study published in Environmental Health Perspectives blood pressure, heart rate, and cardiac biomarkers and the correlation with air pollution was studied. The dependent variable being the blood pressure, heart rate, and biomarkers, and the independent variable was exposure to air pollution. This study took place between 1995-2013. The results state “We observed some evidence suggesting distributional effects of traffic-related pollutants on systolic blood pressure, heart rate variability, corrected QT interval, low density lipoprotein (LDL) cholesterol, triglyceride, and intercellular adhesion molecule-1 (ICAM-1)”. There conclusion also uses subjective words such as “may effect” (Bind, Peters, Koutrakis, Coull, Vokonas, and Schwartz, 2016). With this in mind and the lack of knowledge of other factors related to the participants health I would say it is difficult to exclude the possibility of coincidence in this specific study.

References:

Bind, M., Peters, A., Koutrakis, P., Coull, B., Vokonas, P., & Schwartz, J. (2016). Quantile Regression Analysis of the Distributional Effects of Air Pollution on Blood Pressure, Heart Rate Variability, Blood Lipids, and Biomarkers of Inflammation in Elderly American Men: The Normative Aging Study. Environmental Health Perspectives. https://ehp.niehs.nih.gov/doi/10.1289/ehp.1510044#:~:text=Results%20%20%20%20Outcomes%20%20%20,%20%20%20%2014%20more%20rowsLinks to an external site.

Holmes, A., Illowsky, B., & Dean, S. (2017). Introductory Business Statistics. OpenStax.

Sample Answer 2 for MATH 225N Week 8 Discussion: Correlation and Regression

Both correlation and regression analysis are applied in the determination of the relationship that exist between variables. In both cases, the variables need to be normally distributed and possess a normal distribution. However, there is the difference between the two statistical approaches (Kasuya, 2019). While correlation is only used to measure the association between two continuous variables, regression analysis is used to determine relationship between one dependent variable and one or more independent variables. Additionally, regression analysis is how we measure cause and affect relationships and determine if they are statistically sound or not. Correlation alone is not causation and that is why patterns and influence must be studied (Kasuya, 2019). Performing regression analysis in Body Mass Index (BMI) requires the consideration of different independent variables. Apart from diet and the rate of physical activities, another possible independent variable would be height of an individual or the study participants. Height is always considered in the computation of the BMI, therefore, it is one of the independent variables for the BMI. Also, the values of height are always continuous. However, data analyst need to ensure that there is a normal distribution. 

Physical activities are known to reduce body mass index. In other words, continuous physical activities always aids in the breakdown of excessive body fast that contribute to the increase in BMI. Also, excessive or overeating and overconsumption of junk or fatty foods have been established as the major contributors to increase in BMI. Before undertaking correlation and regression analysis, there is always the need to undertake normality tests to ensure that both the dependent and independent variables meets the requirements for undertaking parametric tests or inferential statistical analysis.   

Reference

Kasuya, E. (2019). On the use of r and r squared in correlation and regression (Vol. 34, No. 1, pp. 235-236). Hoboken, USA: John Wiley & Sons, Inc. Retrieved from: https://esj-journals.onlinelibrary.wiley.com/doi/abs/10.1111/1440-1703.1011Links to an external site.

Sample Answer 3 for MATH 225N Week 8 Discussion: Correlation and Regression

MY TAKE ON REGRESSION EQUATIONS AND RESIDUALS ( ERRORS OF PREDICTION )

Hi Friends and Greetings !!

The regression coefficients are calculated from sample data using the least squares regression procedure.

We get the slope and the vertical intercept of the regression line ( the prediction equation ) from the sample data.

The residuals are the errors of prediction, and since the theoretical sum of the residuals is exactly zero, then in general some of the residuals are negative and some of the residuals are positive.

Please see these slides for more about the prediction equation ( regression equation ) .

Note particularly the slide which visually demonstrates why some of the residuals are positive and some of the residuals are negative.

Thanks Friends and Best Wishes and Good Luck this Week 8 !!

😉

Introductory Business Statistics Holmes Illowsky Dean 2018-8c376461-2f23-4216-9e3b-6d451cf46713.pdf

Sample Answer 4 for MATH 225N Week 8 Discussion: Correlation and Regression

I found an excellent article in our library that compared different regression models for the best approach to predicting BMI: “Factors associated with overweight: are the conclusions influenced by choice of the regression method?” (Juvanhol et al., 2016).  The bottom line was the authors recommend using a combination of different approaches, as these furnish complementary information to the multifactorial predictors of obesity. The article was a little over my head as it discussed gamma regression, which I couldn’t find in our textbook, and quantiles, which also is not in our text but seems a lot like quartiles. But thanks to this course, I was able to understand more of this article than I would have before this course.

In this article, BMI distribution percentiles is on the x-axis of the following charts. The along the y-axis were the values of the estimated coefficients for age, physical inactivity, years of night-shift work, BMI at age 20, domestic overload (cleaning/cooking/laundry factored by number of residents at home) and self-rated health.  According to Juvanhol et al., (2016), these were the explanatory variables. This is still a little confusing to me, as Holmes et al. (2018) stated that a multivariate model or system is where more than one independent variable is used to predict an outcome, and there can only be one dependent variable, but unlimited independent variables. So why did the authors refer to age, etc., as explanatory variables, which would made them independent variables, but not put them on the x-axis?

Anyway, the independent variables are along the y-axis, and are shown in units of the values of the coefficients estimated. Coefficients provide an estimate of the impact of a unit change in the independent variable on the dependent variable (Holmes et al., 2018). The coefficient we use in a linear regression is the slope, or the rise over the run. However, this week we learned about another kind of coefficient, the coefficient of determination which is the explained variation over the total variation (Chamberlain University, 2021). I am not sure which coefficient the authors are referring to in the article.

The grey shaded areas around each line show the 95% confidence interval for the quantile estimates. It is interesting to note the narrowness of the spread of the confidence interval around the line in the “Age” graph and the “BMI at age 20” graphs in comparison to the other four graphs even though they are all at the 95% confidence level. We all know now that a narrow confidence interval is preferred over a wide one (Holmes et al., 2018).

To answer the final question, which statistic would show the value of that regression line in understanding BMI, I’d give more weight (pardon the pun) to the statistics of “Age” and “BMI at age 20” due to the narrowness of the confidence intervals, but also interesting is the way the “Years worked at night” regression line jumps at about the 80^th quantile showing a suddenly stronger association in the upper quantiles. That would be an interesting area to investigate.

Elaine

Chamberlain University. (2021). MATH225. Week 8 Slide Deck [Online lesson]. Downers Grove, IL: Adtalem.

Holmes, A., Illowsky, B., & Dean, S.  (2018).  Introductory business statistics.  OpenStax.

Juvanhol, L.L., Lana, R.M., Cabrelli, R., Bastos, L.S., Nobre, A.A., Rotenberg, L., Griep, R.H. (2016). Factors associated with overweight: are the conclusions influenced by choice of the regression method? BMC Public Health 16, 642. http://doi.org/10.1186/s12889-016-3340-2Links to an external site.