Chapter 11 - Correlation and Regression: Measuring and Predicting Relationships

Abstract

In this chapter you will learn how to recognize and work with the various types of structures we find in bivariate data: a linear (straight-line) relationship, no relationship, a nonlinear relationship, unequal variability, clustering, and outliers. By exploring your data using a scatterplot, you can gain additional insights beyond the conventional statistical summaries. There are two basic approaches to summarizing bivariate data: correlation analysis summarizes the strength of the relationship between the two factors, whereas regression analysis shows you how to use that relationship to predict or control one of the variables using the other. There are two measures of the performance of a regression analysis: the standard error of estimate will tell you the typical size of the prediction errors, whereas the coefficient of determination (equal to the square of the correlation r) tells you the percentage of the variability of the Y variable that is “explained by” the X variable. Statistical inference in regression analysis uses the linear model to produce confidence intervals in the usual way for the estimated effects based on their standard errors. Inference also leads to hypothesis testing, which takes a closer look now at the relationship that appears to exist in the data and helps you decide either that the relationship is significant (and worth your managerial time) or that it could reasonably be due to randomness alone.