76 CHAPTER 2 Exploring Data with Tables and Graphs Correlation Between Shoe Print Lengths and Heights? EXAMPLE 4 Consider the data in Table 2-10 (using data from Data Set 9 “Foot and Height” in Appendix B). From the accompanying scatterplot of the paired data in Table 2-10, it isn’t very clear whether there is a linear correlation. The Statdisk display of the results shows that the linear correlation coefficient has the value of r = 0.591 (rounded). YOUR TURN. Do Exercise 9 “Linear Correlation Coefficient.” TABLE 2-10 Shoe Print Lengths and Heights of Males Shoe Print Length (cm) 29.7 29.7 31.4 31.8 27.6 Height (cm) 175.3 177.8 185.4 175.3 172.7 Statdisk In Example 4, we know from the Statdisk display that in using the five pairs of data from Table 2-10, the linear correlation coefficient is computed to be r = 0.591. Use the following criteria for interpreting such values. Using Table 2-11 to Interpret r: Consider critical values from Table 2-11 as being both positive and negative, and draw a graph similar to Figure 2-17. Use the values in the table for determining whether a value of a linear correlation coefficient r is “close to” 0 or “close to” -1 or “close to” 1 by applying the following criteria: Correlation If the computed linear correlation coefficient r lies in the left or right tail region bounded by the table value for that tail, conclude that there is sufficient evidence to support the claim of a linear correlation. No Correlation If the computed linear correlation coefficient r lies between the two critical values, conclude that there is not sufficient evidence to support the claim of a linear correlation. Figure 2-17 shows that the linear correlation coefficient of r = 0.591 computed from the paired sample data is a value that lies between the critical values of r = -0.878 and r = 0.878 (found from Table 2-11). Figure 2-17 shows that we can consider the value of r = 0.591 to be close to 0 instead of being close to -1 or close to 1. Therefore, there is not sufficient evidence to conclude that there is a linear correlation between shoe print lengths and heights of males.
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