Correlation and Regression

In chapter 3 we focused on summarizing and describing data from a single variable. But often we will need to summarize and describe the relationship between two (or more) variables. Data collected from one variable is known as univariate data, and data collected from two variables is called bivariate data. Our goal is to find a relationship between the two variables, if there is one, or to state that the variables are not related. To do this, we will use:

•Scatter Plots to visualize possible relationships

•Correlation to measure how close the data are to a line

•Regression to make predictions when the data follow a linear pattern

Chapter 4 is a continuation of the third step in the process of statistics, organizing and describing data. What is different in chapter 4 is that there are two quantitative variables instead of one, as there was in chapter 3.

Figure 4.1: The process of statistics

Section 4.1 will discuss how to visualize bivariate data using scatterplots and correlation. Section 4.2 will discuss how to model the relationships between variables using simple linear regression. Section 4.3 will go into more detail regarding the differences between what we predict and observe, and how to measure the effectiveness of the regression model.

By the end of this chapter, you will be able to:

•Describe and interpret the relationship between explanatory and response variables using a scatterplot

•Describe and interpret correlation and association

•Determine when a correlation is statistically significant

•Describe the process of regression

•Identify when it is appropriate to use a least squares regression line for predictions

•Use technology to calculate correlation and the least squares regression line

•Use a regression line to make a prediction

•Describe, calculate, and interpret residuals

•Describe and interpret the coefficient of determination