10-2 Regression 531 SOLUTION REQUIREMENT CHECK (1) The data are a simple random sample. (2) The scatterplot in Figure 10-1 on page 509 shows that the pattern of points is reasonably close to a straight-line pattern. (3) The scatterplot also shows that there are no outliers. The requirements are satisfied. Technology The use of technology is recommended for finding the equation of a regression line. Shown below are the results from different technologies. Minitab and XLSTAT provide the actual equation; the other technologies list the values of the y-intercept and the slope. All of these technologies show that the regression equation can be expressed as yn = -10.9 + 0.174x, where yn is the predicted number of tickets sold and x is the amount of the jackpot. TABLE 10-1 Lottery 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 Statdisk Excel (XLSTAT) Minitab TI-83, 84 Plus StatCrunch SPSS JMP We should know that the regression equation is an estimate of the true regression equation for the population of paired data. This estimate is based on one particular set of sample data, but another sample drawn from the same population would probably lead to a slightly different equation. YOUR TURN. Do Exercise 13 “Powerball Jackpots and Tickets Sold.” Table 10-1 from the Chapter Problem is reproduced here. (Jackpot amounts are in millions of dollars and numbers of tickets sold are in millions.) Use technology to find the equation of the regression line in which the explanatory variable (or x variable) is the amount of the lottery jackpot and the response variable (or y variable) is the corresponding number of lottery tickets sold. CP EXAMPLE 1 Using Technology to Find the Regression Equation
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