2-4 Scatterplots, Correlation, and Regression 73 22. TV and Digital Ads Listed below are amounts (billions of dollars) spent on TV and digital advertising. The amounts are listed in order by year ending with the year 2022. The last few years are projected amounts (based on data from Magna Global). Construct a graph that reveals the story that the data are trying to tell. What story does the graph depict? TV Ads: 94.5 106.3 103.7 109.6 114.3 125.5 131.0 137.6 142.0 143.2 133.1 151.2 157.3 165.6 169.7 176.2 176.2 178.4 178.5 183.0 179.8 183.8 180.0 183.4 Digital Ads: 4.8 9.3 8.5 8.1 11.1 15.5 22.2 32.0 43.3 50.6 52.7 62.6 75.5 89.0 105.2 125.6 150.7 178.4 208.8 236.8 263.9 291.3 319.4 347.7 Key Concept This section introduces the analysis of paired sample data. In Part 1 of this section we discuss correlation and the role of a graph called a scatterplot. In Part 2 we provide an introduction to the use of the linear correlation coefficient. In Part 3 we provide a very brief discussion of linear regression, which involves the equation and graph of the straight line that best fits the sample paired data. All of the principles discussed in this section are discussed more fully in Chapter 10, but this section serves as a quick introduction to some important concepts of correlation and regression. This section does not include details for executing manual calculations, which are rarely done. Instructions for using technology to obtain results are included in Chapter 10. 2-4 Scatterplots, Correlation, and Regression PART 1 Scatterplot and Correlation Our objective in this section is to explore whether there is a correlation, or association, between two variables. We begin with basic definitions. DEFINITIONS A correlation exists between two variables when the values of one variable are somehow associated with the values of the other variable. A linear correlation exists between two variables when there is a correlation and the plotted points of paired data result in a pattern that can be approximated by a straight line. A scatterplot (or scatter diagram) is a plot of paired (x, y) quantitative data with a horizontal x-axis and a vertical y-axis. The horizontal axis is used for the first variable (x), and the vertical axis is used for the second variable (y). CAUTION The presence of a correlation between two variables is not evidence that one of the variables causes the other. We might find a correlation between beer consumption and weight, but we cannot conclude from the statistical evidence that drinking beer has a direct effect on weight. Correlation does not imply causality!
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