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# 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.

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

# Learning Resources

Frankfort-Nachmias, C., & Leon-Guerrero, A. (2018). Social statistics for a diverse society (8th ed.). Thousand Oaks, CA: Sage Publications.

• Chapter 12, “Regression and Correlation” (pp. 325-371)

Wagner, III, W. E. (2020). Using IBM® SPSS® statistics for research methods and social science statistics (7th ed.). Thousand Oaks, CA: Sage Publications.

• Chapter 8, “Correlation and Regression Analysis”

Document: Walden University: Research Design Alignment Table

#### Datasets

Document: Data Set 2014 General Social Survey (dataset file)
Use this dataset to complete this week’s Discussion.
Note: You will need the SPSS software to open this dataset.

#### Required Media

Laureate Education (Producer). (2016b). Correlation and bivariate regression [Video file]. Baltimore, MD: Author.
Note: The approximate length of this media piece is 9 minutes.
In this media program, Dr. Matt Jones demonstrates correlation and bivariate regression using the SPSS software.

#### Optional Resources

Correlation
https://istats.shinyapps.io/guesscorr/
Use the following app/weblink for an interactive visual display of correlation slopes.

Regression
https://istats.shinyapps.io/ExploreLinReg/
Use the following app/weblink for an interactive visual display of regression slopes.

Skill Builder: Interpreting Correlation and Regression Coefficients
To access these Skill Builders, navigate back to your Blackboard Course Home page, and locate “Skill Builders” in the left navigation pane. From there, click on the relevant Skill Builder link for this week.

You are encouraged to click through these and all Skill Builders to gain additional practice with these concepts. Doing so will bolster your knowledge of the concepts you’re learning this week and throughout the course.

# 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?

## Expert Solution Preview

Introduction:

This week’s content focuses on correlation and bivariate regression. Students will learn how to construct research questions, evaluate research design, and analyze results related to correlation and bivariate regression. They will also learn how to analyze measures for correlation and bivariate regression, analyze significance, and evaluate research related to correlation and bivariate regression. To apply the concepts learned, students will analyze datasets and conduct a critique on an article related to correlation or regression.

1. What is the research design used by the authors?

The authors used a correlational research design. They aimed to investigate the relationship between two variables and the degree to which they are associated. Correlational research designs are useful when researchers want to examine the strength and direction of the relationship between variables without manipulating them. The correlation coefficient indicates the degree of association between variables, and the authors used it to determine the extent to which the two variables are related.

2. Why did the authors use correlation or bivariate regression? Do you think it’s the most appropriate choice? Why or why not?

The authors used correlation or bivariate regression because they wanted to investigate the relationship between two variables. Correlation is used to measure the strength and direction of the relationship between two variables. Bivariate regression, on the other hand, is used to determine the extent to which one variable predicts the other. I believe the authors made the appropriate choice by using correlation or bivariate regression because they are widely used statistical tests for investigating relationships between variables.

3. Did the authors display the data? Do the results stand alone? Why or why not?

The authors displayed the data using scatterplots and also showed the correlation coefficient values. The results stand alone because the correlation coefficient indicates the strength and direction of the relationship between variables. However, it would be beneficial for the authors to include a table with means and standard deviations of each variable to give the readers more information about the variables being examined.

4. Did the authors report effect size? If yes, is this meaningful?

The authors reported effect size in the form of a correlation coefficient. The correlation coefficient indicates the strength and direction of the relationship between variables. Effect size is meaningful because it allows readers to determine the practical significance of the relationship between variables. By including effect size, readers can determine if the observed relationship is large or small, which is essential for making informed decisions based on the results.

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