10-1 Correlation 513 SPSS YOUR TURN. Do Exercise 13 “Powerball Jackpots and Tickets Sold.” TABLE 10-2 Calculating r with Formula 10-1 x (Jackpot) y (Tickets) x2 y2 xy 334 54 111,556 2916 18,036 127 16 16,129 256 2032 300 41 90,000 1681 12,300 227 27 51,529 729 6129 202 23 40,804 529 4646 180 18 32,400 324 3240 164 18 26,896 324 2952 145 16 21,025 256 2320 255 26 65,025 676 6630 Σx = 1934 Σy = 239 Σx2 = 455,364 Σy2 = 7691 Σxy = 58,285 Use Formula 10-1 to find the value of the linear correlation coefficient r for the Powerball jackpot amounts and numbers of tickets listed in Table 10-1. CP YOUR TURN. Do Exercise 13 “Powerball Jackpots and Tickets Sold.” EXAMPLE 2 Finding r Using Formula 10-1 SOLUTION Using Formula 10-1, the value of r is calculated as shown below. Here, the variable x is used for the jackpot amount, and the variable y is used for the numbers of lottery tickets. Because there are 9 pairs of data, n = 9, and the other required values are computed in Table 10-2. Using Formula 10-1 with the paired data from Table 10-1, r is calculated as follows: r = nΣxy - 1Σx21Σy2 2 n1Σx22 - 1Σx222n1Σy22 - 1Σy22 = 9158,2852 - 11934212392 2 91455,3642 - 119342229176912 - 123922 = 62,339 2 357,920212,098 = 0.947 Speeding Out-of-Towners Ticketed More? Are police more likely to issue a ticket to a speeding driver who is out-of-town than to a local driver? George Mason University researchers Michael Makowsky and Thomas Stratmann addressed this question by examining more than 60,000 warnings and tickets issued by Massachusetts police in one year. They found that out-of-town drivers from Massachusetts were 10% more likely to be ticketed than local drivers, and the 10% figure rose to 20% for out-ofstate drivers. They also found a statistical association between a town’s finances and speeding tickets. When compared to local drivers, out-of-town drivers had a 37% greater chance of being ticketed when speeding in a town in which voters had rejected a proposition to raise taxes more than the 2.5% amount allowed by the state levy limit. M
RkJQdWJsaXNoZXIy NjM5ODQ=