Example 16.4 The data given in Table 16.4 are used to calculate the correlation coefficient. Tahle 165 shows the worksheet for this purpose. This is followed by the calculation of correlation coefficient Table 16.5 Computation of Correlation Coefficient 5-15 15-25 25-35 35-45 Total Y MV 10 20 30 40 MV dx → -1 1 2 fdy fdy? fáxdy dy I 75-125 100 3(3) 8(0) 2(-2) 3(-6) -1 4(0) 6(0) 2(0) 3(0) 4(-4) 8(-16) 19 -19 19 -17 125-175 150 5(0) 7(0) 4(8) 2(8) 26 175-225 200 1 3(3) 2(4) 11 11 11 225-275 250 10 20 40 6. Total 16 15 14 21 66 12 70 -2 fdx fdx? fdxdy -16 14 42 40 16 14 84 114 -5 Check 3 0. -2 o o o

Chapter 4 Homework Score: 3/14 3/14 answered Question 1 Based on the data shown below, calculate the correlation coefficient (to three decimal places) y 4 27.54 26.8 27.96 29.02 31.68 9. 34.24 Question Help: MMessage instructor Submit Question 5678

2. For this question use the following set of data points. Use Excel's CORREL function to find the value of the correlation coefficient. 1 1 2 2 3 3 3 10 1 2 3 1 3 1 2 3 10 (a) Obtain a scatter plot of the 10 data points. (b) Find the value of the correlation coefficient for the 10 data points. (c) Use Excel with a = 0.05 to determine if there is a linear correlation. Now remove the point with coordinates (10, 10) so there are 9 pairs of points. (d) Obtain a scatter plot of the 9 data points. (e) Find the value of the correlation coefficient for the 9 data points. (f) Use Excel with a = 0.05 to determine if there is a linear correlation. (g) What conclusion do you make about the possible effect of a single pair of values?

Consider the following table of data. 2 3 4 y 1 1 1 1.1 (a) Calculate the correlation coefficient. (b) Sketch a graph of the data. (c) Based on how closely the data fits a straight line, is your answer to part (a) surprising? Discuss the extent to which the correlation coefficient describes how well the data fit a horizontal line.

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After gathering data about the number of starfish and measuring the pollution in areas of the ocean you find a negative linear correlation between pollution levels and number of starfish. What can you conclude based on this information? a. There is a confounding variable that is affecting both pollution and starfish. b. As pollution rises the number of starfish falls c. That pollution is causing starfish to die, leading to the negative correlation d. That pollution is supporting starfish, leading to the negative correlation

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