SECTION 9.1 Correlation 471 GDP (in trillions of dollars), x CO2 emissions (in millions of metric tons), y 1.7 620.1 2.4 475.2 3.0 457.6 1.2 389.7 4.1 810.8 2.3 352.9 0.9 235.0 1.8 297.8 2.9 413.9 5.4 1216.5 x Hours of exercise Grade point average y 2 4 6 8 1012141618 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Constructing a Scatter Plot A researcher wants to determine whether there is a linear relationship between a country’s gross domestic product (GDP) and carbon dioxide (CO2) emissions. The data for 10 different countries in a recent year are shown in the table at the left. Display the data in a scatter plot and describe the type of correlation. (Source: U.S. Energy Information Administration) SOLUTION The scatter plot is shown below. From the scatter plot, it appears that there is a positive linear correlation between the variables. x GDP (in trillions of dollars) CO2 emissions (in millions of metric tons) y 1 2 3 4 5 6 200 400 600 800 1000 1200 1400 Interpretation As the gross domestic products increase, the carbon dioxide emissions tend to increase. TRY IT YOURSELF 1 A director of alumni affairs at a small college wants to determine whether there is a linear relationship between the number of years alumni have been out of school and their annual contributions (in thousands of dollars). The data are shown in the table below. Display the data in a scatter plot and describe the type of correlation. Number of years out of school, x 11051532430 Annual contribution (in thousands of dollars), y 12.5 8.7 14.6 5.2 9.9 3.1 2.7 Answer: Page A42 Constructing a Scatter Plot A student conducts a study to determine whether there is a linear relationship between the number of hours a student exercises each week and the student’s grade point average (GPA). The data are shown in the table below. Display the data in a scatter plot and describe the type of correlation. Hours of exercise, x 123 0 61021814155 GPA, y 3.6 4.0 3.9 2.5 2.4 2.2 3.7 3.0 1.8 3.1 SOLUTION The scatter plot is shown at the left. From the scatter plot, it appears that there is no linear correlation between the variables. Interpretation The number of hours a student exercises each week does not appear to be related to the student’s grade point average. EXAMPLE 1 EXAMPLE 2 Tech Tip Remember that all data sets containing 20 or more entries are available electronically. Also, some of the data sets in this section are used throughout the chapter, so save any data that you enter. For instance, the data used in Example 1 are also used later in this section and in Sections 9.2 and 9.3.
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