10-1 Correlation 521 Shown below is Table 10-1 from the Chapter Problem, followed by two resamplings in which the ticket data are shuffled in a random order. Such shuffles are based on the null hypothesis of no correlation, and if we calculate the linear correlation coefficient r for each new shuffle, we get a list of r values that can be used to determine whether the actual r = 0.947 from the original data in Table 10-1 is significant in the sense that it is not likely to occur by chance when there really is no correlation. 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 Random shuffling of ticket data: Tickets 16 54 16 26 18 27 41 23 18 Another random shuffling of ticket data: Tickets 18 16 54 27 41 23 18 16 26 Using the paired data in Table 10-1, we can use technology to create 1000 samples using the preceding method of shuffling. Here is one result from technology: Among the 1000 values of r created by shuffling the ticket values as described above, none of them are at least as extreme as the value of r = 0.947 found from the original data in Table 10-1. Because a result of r = 0.947 never occurred among 1000 samples, it appears that the likelihood of such an extreme value is around 0.000. This shows that a value such as r = 0.947 is significant in the sense that it is not likely to occur by chance. This suggests that there is a correlation between the jackpot amounts and the numbers of tickets sold. Correlation Access tech supplements, videos, and data sets at www.TriolaStats.com TECH CENTER Statdisk 1. Click Analysis in the top menu. 2. Select Correlation and Regression from the dropdown menu. 3. Enter the desired significance level and select the columns to be evaluated. 4. Click Evaluate. 5. Click Scatterplot to obtain a scatterplot with the regression line included. StatCrunch 1. Click Stat in the top menu. 2. Select Regression from the dropdown menu, then select Simple Linear from the submenu. 3. Select the columns to be used for the x variable and y variable. 4. Click Compute! 5. Click the arrow at the bottom of the results window to view the scatterplot. Minitab 1. Click Stat in the top menu. 2. Select Basic Statistics from the dropdown menu and select Correlation from the submenu. 3. Select the columns to be evaluated under Variables. 4. Click the Options button, select Pearson correlation for Method and enter the desired confidence level. 5. Click OK twice. Scatterplot 1. Click Stat in the top menu. 2. Select Regression—Fitted Line Plot from the dropdown menu. 3. Select the desired columns for the y variable and x variable. 4. Select Linear under Type of Regression Model and click OK. TIP: Another procedure is to click on Assistant in the top menu, then select Regression and Simple Regression. Complete the dialog box to get results. continued
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