Correlation 9.1 470 CHAPTER 9 Correlation and Regression What You Should Learn An introduction to linear correlation, independent and dependent variables, and the types of correlation How to find a correlation coefficient How to test a population correlation coefficient r using a table How to perform a hypothesis test for a population correlation coefficient r How to distinguish between correlation and causation An Overview of Correlation Correlation Coefficient Using a Table to Test a Population Correlation Coefficient r Hypothesis Testing for a Population Correlation Coefficient r Correlation and Causation An Overview of Correlation Suppose a safety inspector wants to determine whether a relationship exists between the number of hours of training for an employee and the number of accidents involving that employee. Or suppose a psychologist wants to know whether a relationship exists between the number of hours a person sleeps each night and that person’s reaction time. How would he or she determine if any relationship exists? In this section, you will study how to describe what type of relationship, or correlation, exists between two quantitative variables and how to determine whether the correlation is significant. A correlation is a relationship between two variables. The data can be represented by the ordered pairs 1x, y2, where x is the independent (or explanatory) variable and y is the dependent (or response) variable. DEFINITION In Section 2.2, you learned that the graph of ordered pairs 1x, y2 is called a scatter plot. In a scatter plot, the ordered pairs 1x, y2 are graphed as points in a coordinate plane. The independent (explanatory) variable x is measured on the horizontal axis, and the dependent (response) variable y is measured on the vertical axis. A scatter plot can be used to determine whether a linear (straight line) correlation exists between two variables. The scatter plots below show several types of correlation. x As x increases, y tends to increase. y x As x increases, y tends to decrease. y Positive Linear Correlation Negative Linear Correlation x y x y No Correlation Nonlinear Correlation
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