Correlation and Regression

The Pearson Correlation is introduced as a measure of the degree of relationship between two continuous variables. We emphasize to students that one cannot assume a causal relationship simply because two variables are correlated: it is possible that changing one variable causes changes in the other, but there could also be relationship between those variables and a third variable. The strength and direction of the relationship are introduced in the context of graphing correlations on a scatterplot, with illustrations showing scatterplots of positive and negative correlations and no relationship. An example association between the behavior of young children and the time they spent napping provides the context for discussing calculations, using a small data set. Students are instructed in calculating the necessary preliminary statistics, such as sums of scores, sums of squared scores, and the sum of the XY products. The formula for Pearson’s r is introduced and students are guided through applying it, step-by-step, to solve for the obtained value of r. Via hypothesis testing, the obtained value of r is compared to the critical value, found on the table of critical values for the Pearson Correlation. The effect size, r2, is calculated, results are presented in APA (seventh edition) formatting, and interpretation is discussed. An additional example is then used to review these concepts and calculations; in this example, we determine whether there is a relationship between time spent walking outdoors and ratings of happiness. Linear regression analysis is briefly summarized. A biography box highlights Karl Pearson, and sidebar notes point out mistakes to avoid. Like the previous chapters, the present chapter also includes a chapter summary, step-by-step instructions on how to compute the Pearson Correlation using Excel’s Data Analysis Toolpak, and critical thinking questions and practice problems.