Correlation and Simple Linear Regression

Abstract

Up until now in this book, you have been dealing with the situation in which you have had only one group or two groups of people (or objects) in your research study and only one measurement (i.e., variable) “number” on each of these people. This chapter asks you to change gears again and to deal with the situation in which you are measuring two variables instead of only one variable and you are trying to discover the “relationship” between these variables. For example, if one variable increases in value, does the other variable increase in value (i.e., a “positive” relationship) or decrease in value (i.e., a negative relationship), and is this relationship “weak” or “strong?” The formula for the correlation r is presented, explained, and the nine steps for computing a correlation are explained using a calculator example. Then, the Excel commands for computing a correlation are presented along with the Excel steps needed to create a chart summarizing the relationship between the two variables. You will learn how to use Excel to draw the “best-fit line” through the data points on a scatterplot and how to determine the equation for this line so that you can use this equation to predict one variable from the other variable. You will learn both how to print a chart by itself, and how to print both the table and the chart so that they fit onto a single page, how to print only the chart by itself on a separate page, and how to print only the SUMMARY OUTPUT of the regression analysis so that it fits onto a separate page by itself. Three practice problems are given at the end of the chapter to test your Excel skills, and the answers to these problems appear in Appendix A of this book. An additional practice problem is presented in the Practice Test given in Appendix B along with its answer in Appendix C of this book.