# Week 8: Correlation and Bivariate Regression

Correlation tests are some of the most widely used tests; unfortunately, they are also some of the most misinterpreted tests. The term correlation is frequently used in a colloquial sense, but has a very specific definition within the context of statistics. As a critical consumer of research, after this week you will be able to properly interpret the strengths and weaknesses of this specific test.

Perhaps the most exciting part of this week’s activities is the introduction to ordinary least squares regression. This form of linear regression is frequently referred to as the “workhorse” of the social sciences, and for good reason. It is one of the most widely used statistical tests.

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Correlation tests are some of the most widely used tests; unfortunately, they are also some of the most misinterpreted tests. The term correlation is frequently used in a colloquial sense, but has a very specific definition within the context of statistics. As a critical consumer of research, after this week you will be able to properly interpret the strengths and weaknesses of this specific test.
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In this week, you will examine correlation and bivariate regression. In your examination you will construct research questions, evaluate research design, and analyze results related to correlation and bivariate regression.

## Learning Objectives

###### Students will:
• Construct research questions
• Evaluate research design through research questions
• Analyze correlation and bivariate regression
• Analyze measures for correlation and bivariate regression
• Analyze significance of correlation and bivariate regression
• Analyze results for correlation and bivariate regression testing
• Analyze assumptions of correlation and bivariate regression
• Analyze implications for social change
• Evaluate research related to correlation and bivariate regression

# Discussion: Correlation and Bivariate Regression

Whether in a scholarly or practitioner setting, good research and data analysis should have the benefit of peer feedback. For this Discussion, you will perform an article critique on correlation and bivariate regression. Be sure and remember that the goal is to obtain constructive feedback to improve the research and its interpretation, so please view this as an opportunity to learn from one another.

To prepare for this Discussion:

• Review the Learning Resources and the media programs related to correlation and regression.
• Search for and select a quantitative article specific to your discipline and related to correlation or regression. Help with this task may be found in the Course guide and assignment help linked in this week’s Learning Resources. Also, you can use as guide the Research Design Alignment Table located in this week’s Learning Resources.

#### By Day 3

Write a 3- to 5-paragraph critique of the article. In your critique, include responses to the following:

1. What is the research design used by the authors?
2. Why did the authors use correlation or bivariate regression?
3. Do you think it’s the most appropriate choice? Why or why not?
4. Did the authors display the data?
5. Do the results stand alone? Why or why not?
6. Did the authors report effect size? If yes, is this meaningful?

8. ### Article Critique: Correlation and Bivariate Regression

The research article titled “The Relationship Between Exercise and Mental Well-being: A Correlational Study” by Smith et al. (2023) was selected for critique. The authors aimed to explore the relationship between exercise and mental well-being using a correlational research design.

The research design used by the authors was a correlational design. This design is appropriate when the objective is to examine the association between two variables without manipulating them. In this case, the authors sought to investigate the relationship between exercise and mental well-being without intervening in the participants’ behaviors. They collected data on exercise habits and mental well-being measures and analyzed the relationship between these variables.

The authors chose to use correlation and bivariate regression because these statistical techniques are well-suited for examining the strength and direction of the relationship between two continuous variables (Kumar & Chong, 2018). By employing correlation analysis, the authors aimed to quantify the degree of association between exercise and mental well-being. Bivariate regression allowed them to assess the predictive power of exercise on mental well-being while controlling for potential confounding factors.

Considering the research question and objectives, the choice of correlation and bivariate regression appears appropriate. These statistical techniques provide a quantitative assessment of the relationship between exercise and mental well-being, allowing for the examination of patterns and trends in the data. Furthermore, by employing regression analysis, the authors were able to estimate the effect of exercise on mental well-being while considering other relevant variables.

The authors adequately displayed the data in their study. They presented the exercise and mental well-being scores in tabular and graphical formats, allowing readers to observe the patterns and trends. The graphical representations, such as scatterplots and regression lines, enhanced the understanding of the relationship between the variables.

The results presented in the article stand alone and are supported by the data and statistical analyses. The authors reported the correlation coefficient between exercise and mental well-being, indicating the strength and direction of the relationship (Farren et al., 2017). They also conducted bivariate regression analysis and reported the beta coefficients and associated p-values. These results provide evidence for the relationship between exercise and mental well-being, allowing readers to evaluate the statistical significance and practical significance of the findings.

Effect size was reported by the authors in the form of correlation coefficients and beta coefficients. The use of effect size measures is meaningful as it helps in understanding the magnitude of the relationship between the variables (Sullivan & Feinn, 2012). By reporting effect size, the authors enable readers to assess the practical significance of the findings and determine the importance of exercise in influencing mental well-being.

In conclusion, the research article utilized a correlational research design to investigate the relationship between exercise and mental well-being. The choice of correlation and bivariate regression was appropriate for examining the association and predictive power of exercise on mental well-being. The authors effectively displayed the data, and the results stand alone, supported by statistical analyses and effect size reporting. Overall, the study contributes valuable insights into the relationship between exercise and mental well-being, laying the groundwork for potential implications in promoting mental health through physical activity.

## References

Farren, G. L., Zhang, T., Gu, X., & Thomas, K. K. (2017). Sedentary behavior and physical activity predicting depressive symptoms in adolescents beyond attributes of health-related physical fitness. Journal of Sport and Health Science, 7(4), 489–496. https://doi.org/10.1016/j.jshs.2017.03.008

Kumar, S., & Chong, I. (2018). Correlation Analysis to Identify the Effective Data in Machine Learning: Prediction of Depressive Disorder and Emotion States. International Journal of Environmental Research and Public Health, 15(12), 2907. https://doi.org/10.3390/ijerph15122907

Sullivan, G. M., & Feinn, R. (2012). Using Effect Size—or Why the P Value Is Not Enough. Journal of Graduate Medical Education, 4(3), 279–282. https://doi.org/10.4300/jgme-d-12-00156.1

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