4. (22 points) Table 1 presents four sets of data prepared by the statistician Frank Anscombe to illustrate the dangers

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4 22 Points Table 1 Presents Four Sets Of Data Prepared By The Statistician Frank Anscombe To Illustrate The Dangers 1 (64.89 KiB) Viewed 42 times

4. (22 points) Table 1 presents four sets of data prepared by the statistician Frank Anscombe to illustrate the dangers of calculating without first plotting the data. Among the four, three data sets have the same correlation and the same least-squares regression line to several decimal places. The regression equation is y - 3+0.5x (a) Make a scatterplot for each of the four data sets and draw the regression line on cach of the plots using excel. (If you want to draw the regression line by hand, substitute x = 5 and x = 10 into the equation. Find the predicted y for each . Plot these two points and draw the line through them on all four plots.) (b) Describe in words the direction, form, and strength of the relationship. (e) Compute the correlation coefficient for each data set (you can use Excel). (d) Explain for each scatterplot whether you consider the correlation coefficient provides a meaningful estimate of the form and strength of the relationship (C) In which of the four cases would you be willing to use the regression line to predict y given that x = 10? Explain your answer in each case. Table 1 Four data sets for exploring correlation Data set A X Y 10 8 8.04 6.95 13 9 11 14 6 7.58 8.81 8.33 9.967.24 4 12 4.26 10.84 7 4.82 5.68 Data set B Х Y 10 8 9.14 8.14 13 9 11 8.74 8.77 9.26 14 6 8.1 6.13 4 3.1 12 9.13 7 7.26 5 4.74 Data set C X Y 10 8 7.46 6.77 13 9 11 12.74 7.11 7.81 14 6 8.84 6.08 4 5.39 12 8.15 7 6.42 5 5.73 ON Data set D X Y 10 6.58 8 5.76 13 7.71 9 11 8.84 8.47 14 6 7.04 5.25 4 5.56 127 7.91 6.89 5 12.5 T