Correlation and Regression

Last week you gained an understanding of the importance of examining assumptions prior to conducting statistical analyses that test hypotheses. This week you will move from descriptive analyses and the examination of assumptions to actually conducting such analyses. We will cover analytical strategies common to the field of business: Correlation and Regression.

Correlation is a method used to express the relationship between two variables – that is, as one variable changes, how does the other? For example, you might be interested in studying whether there is a relationship between exercise and illness/disease or employee satisfaction and work productivity.

Regression is a method that uses one variable to predict another (continuous) variable. So, perhaps you are interested in studying stress and want to know if the number of hours spent in yoga classes can explain a significant amount of variance in stress scores. A simple regression can answer this question for you. For most business research questions, you will want to add in other explanatory variables, such as number of hours at work each week, personality style, organizational culture, etc. We will soon learn about multiple regression so mastering these simple techniques will lay a solid foundation for the more advanced ones.

Finally, this assignment covers three chapters, so plan accordingly.

Review the resources listed in the Books and Resources area below to prepare for this week’s assignments.

To Prepare for this week’s assignment
Download the following SPSS Data Set. The visual displays you will be asked to create as part of this Activity are ones you will work through in this chapter.

Chamorro-Premuzic.sav
Read Chapters 7, 8 and 9 in the text. It will be to your advantage to have SPSS open on your computer as you work through these chapters. While you are reading consider your area of research interest and when you have seen correlation and regression applied. How might you use these analytical strategies in your dissertation research?

Complete the Self-Tests in the chapters. Answers are available at: http://www.sagepub.com/field4e/study/selftest.htmb.

Complete Smart Alex’s Quizzes. Answers are available at: http://www.sagepub.com/field4e/study/smartalex.htm.

Optional Preparation for this week’s assignment
After completing the above assignments, if you feel you need additional instruction on the concepts covered, please choose any of the following activities that will assist you in mastering the core concepts.

Interactive Multiple Choice Questions
Flashcards

You will submit one Word document. You will create this Word document by cutting and pasting SPSS output into Word. Please answer the questions first and include all output at the end of the activity in an Appendix.

Part A. SPSS Assignment
Part A of Assignment #3 has you familiarizing yourself with a set of data, providing you the opportunity to perform statistical tests and then interpret the output. You will rely on all you have learned to this point and add correlation and regression strategies to your skill set.

Using the data set: Chamorro-Premuzic.sav; you will focus on the variables related to Extroversion and Agreeableness (student and lecturer).

To complete Part A

Exploratory Data Analysis.
Perform Exploratory Data Analysis on all variables in the data set. Because you are going to focus on Extroversion and Agreeableness, be sure to include scatterplots for these combinations of variables (Student Agreeableness/Lecture Agreeableness; Student Extroversion/Lecture Extroversion; Student Agreeableness/Lecture Extroversion; Student Extroversion/Lecture Agreeableness) and include the regression line within the chart.
Compose a one to two paragraph write up of the data.
Create an APA style table that presents descriptive statistics for the sample.
Make a decision about the missing data. How are you going to handle it and why?
Correlation. Perform a correlational analysis on the following variables: Student Extroversion, Lecture Extroversion, Student Agreeableness, Lecture Agreeableness.
Ensure you handle missing data as you decided above.
State if you are using a one or two-tailed test and why.
Write up the results in APA style and interpret them.
Regression. Calculate a regression that examines whether or not you can predict if a student wants a lecturer to be extroverted using the student’s extroversion score.
Multiple Regression. Calculate a multiple regression that examines whether age, gender, and student’s extroversion predict if a student wants the lecturer to be extroverted.
Ensure you handle missing data as you decided above.
State if you are using a one or two-tailed test and why.
Include diagnostics.
Discuss assumptions: are they met?
Write up the results in APA style and interpret them.
Do these results differ from the correlation results above?
Part B. Applying Analytical Strategies to an Area of Research Interest

Briefly restate your research area of interest.
Pearson Correlation: Identify two variables for which you could calculate a Pearson correlation coefficient. Describe the variables and their scale of measurement. Now, assume you conducted a Pearson correlation and came up with a significant positive or negative value. Create a mock r value (for example, .3 or -.2). Report your mock finding in APA style (note the text does not use APA style) and interpret the statistic in terms of effect size and R2 while also taking into account the third variable problem as well as direction of causality.
Spearman’s Correlation: Identify two variables for which you could calculate a Spearman’s correlation coefficient. Describe the variables and their scale of measurement. Now, assume you conducted a correlation and came up with a significant positive or negative value. Create a mock r value (for example, .3 or -.2). Report your mock finding in APA style and interpret the statistic in terms of effect size and R2 while also taking into account the third variable problem as well as direction of causality.
Partial Correlation vs. Semi-Partial Correlation: Identify three variables for which you may be interested in calculating either a partial or semi-partial correlation coefficient. Compare/contrast these two types of analyses using your variables and research example. Which would you use and why?
Simple Regression: Identify two variables for which you could calculate a simple regression. Describe the variables and their scale of measurement. Which variable would you include as the predictor variable and which as the outcome variable? Why? What would R2 tell you about the relationship between the two variables?
Multiple Regression: Identify at least 3 variables for which you could calculate a multiple regression. Describe the variables and their scale of measurement. Which variables would you include as the predictor variable and which as the outcome variable? Why? Which regression method would you use and why? What would R2 and adjusted R2 tell you about the relationship between the variables?
Logistic Regression: Identify at least 3 variables for which you could calculate a logistic regression. Describe the variables and their scale of measurement. Which variables would you include as the predictor variable and which as the outcome variable? Why? Which regression method would you use and why? What would the output tell you about the relationship between the variables?
Your submittal should demonstrate thoughtful consideration of the ideas and concepts that are presented in the course and provide new thoughts and insights relating directly to this topic. Where applicable your submittal should reflect scholarly writing and current APA standards. Review APA Form and Style.

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