TABLE 10-1 Powerball Tickets Sold and Jackpot Amounts Jackpot 334 127 300 227 202 180 164 145 255 Tickets 54 16 41 27 23 18 18 16 26 When considering the first two of the preceding questions, it is important to recognize that a correlation between two variables does not necessarily imply that one of the variables is the cause of the other. One of the most memorable quotes from introductory statistics courses is that “correlation does not imply causality.” Maybe increasing a lottery jackpot will cause an increase in sales of lottery tickets, but there is no way that we can make that conclusion based on a statistical analysis. The last of the preceding questions involves at least as much common sense as statistical knowledge. Like every topic in statistics, common sense or critical thinking proves to be an indispensable tool. A major focus of this chapter is to analyze paired sample data. In Section 9-3 we considered sample data consisting of matched pairs, but the goal in Section 9-3 was to make inferences about the mean of the differences from the matched pairs. In this chapter we again consider paired sample data, but the objective is fundamentally different from that of Section 9-3. In this chapter we present methods for determining whether there is a correlation, or association, between two variables. For linear correlations, we can identify an equation of a straight line that best fits the data, and we can use that equation to predict the value of one variable given the value of the other variable. Here are the chapter objectives: 10-1 Correlation • Use paired data to find the value of the linear correlation coefficient r. • Determine whether there is sufficient evidence to support a conclusion that there is a linear correlation between two variables. • Use the resampling method of randomization to test a null hypothesis of no correlation. 10-2 Regression • Use paired sample data to find the equation of the regression line. • Find the best predicted value of a variable given some value of the other variable. 10-3 Prediction Intervals and Variation • Use paired sample data to determine the value of the coefficient of determination r2, and to interpret that value. • Use a given value of one variable to find a prediction interval for the other variable. 10-4 Multiple Regression • Interpret results from technology to determine whether a multiple regression equation is suitable for making predictions. • Compare results from different combinations of predictor variables and identify the combination that results in the best multiple regression equation. Chapter Objectives 507 CHAPTER OBJECTIVES >>>
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