Chap013 - C HAPTER 13 L INEAR R EGRESSION AND C ORRELATION...

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Unformatted text preview: C HAPTER 13 L INEAR R EGRESSION AND C ORRELATION 1. 28 5.6 5 X = = 29 5.8 5 Y = = 29.2 2.7 4 x s = = 6.8 1.3 4 y s = = 10.6 0.75 (5 1)(2.7)(1.3) r = =- The 0.75 coefficient indicates a rather strong positive correlation between X and Y . The coefficient of determination is 0.5625, found by (0.75) 2 . X accounts for more than 56 percent of the variation in Y . 2. 39 4.88 8 X = = 85 10.63 8 Y = = 20.88 1.73 7 x s = = 79.88 3.38 7 y s = = 36.38 0.89 (8 1)(1.73)(3.38) r- = = -- The - 0.89 indicates a very strong negative relationship between X and Y . The coefficient of determination if 0.7921, found by (- 0.89) 2 . Nearly X accounts for 80 percent of the variation in Y . Chapter 13 116 X Y ( 29 X X- ( 29 Y Y- ( 29 2 X X- ( 29 2 Y Y- ( 29 ( 29 X X Y Y-- 4 4-1.6-1.8 2.56 3.24 2.88 5 6-0.6 0.2 0.36 0.04-0.12 3 5-2.6-0.8 6.76 0.64 2.08 6 7 0.4 1.2 0.16 1.44 0.48 1 7 4.4 1.2 19.36 1.44 5.28 2 8 2 9 29.2 6.8 10.6 X Y ( 29 X X- ( 29 Y Y- ( 29 2 X X- ( 29 2 Y Y- ( 29 ( 29 X X Y Y-- 5 1 3 0.13 2.38 0.02 5.64 0.30 3 1 5-1.88 4.38 3.52 19.14-8.20 6 7 1.13-3.63 1.27 13.14-4.08 3 1 2-1.88 1.38 3.52 1.89-2.58 4 1 3-0.88 2.38 0.77 5.64-2.08 4 1 1-0.88 0.38 0.77 0.14-0.33 6 9 1.13-1.63 1.27 2.64-1.83 3. a. Sales b. c. 20 4 5 X = = 85 17 5 Y = = 10 1.58 4 x s = = 150 6.12 4 y s = = 36 0.93 (5 1)(1.58)(6.12) r = =- d. The coefficient of determination is 0.8649, found by (0.93) 2 e. There is a strong positive association between the variables. The number of airings explains about 86 percent of the variation in sales. 4. a. b. Yes, as the number of assemblers increases, so does the production. c. 15 3 5 X = = 120 24 5 Y = = 10 1.581 4 x s = = 570 11.937 4 y s = = 70 0.927 (5 1)(1.581)(11.937) r = =- Chapter 13 117 10 20 30 40 1 2 3 4 5 6 Assemblers Production 10 20 30 2 3 4 5 6 Number of Advertisements Sales($000) X Y ( 29 X X- ( 29 Y Y- ( 29 2 X X- ( 29 2 Y Y- ( 29 ( 29 X X Y Y-- 4 1 5-2 4 2 8-2-9 4 81 18 5 2 1 1 4 1 16 4 6 2 4 2 7 4 49 14 1 X Y ( 29 X X- ( 29 Y Y- ( 29 2 X X- ( 29 2 Y Y- ( 29 ( 29 X X Y Y-- 2 15-1-9 1 81 9 4 25 1 1 1 1 1 1 10-2-14 4 196 28 5 40 2 16 4 256 32 3 30 6 36 1 5 12 10 570 70 d. The r 2 is 0.8593, so about 86 percent of the variation in production is explained by the variation in the number of assemblers. 5. a. Police is the independent variable and crime is the dependent variable b. c. 146 18.25 8 X = = 95 11.875 8 Y = = 241.5 5.874 7 x s = = 290.875 6.446 7 y s = = 231.75 0.874 (8 1)(5.874)(6.446) r- = = -- d. 0.76, found by (- 0.874) 2 e. Strong inverse relationship. As the number of police increase, the crime decreases. Chapter 13 118 10 20 30 10 15 20 25 30 Police Crimes X Y ( 29 X X- ( 29 Y Y- ( 29 2 X X- ( 29 2 Y Y- ( 29 ( 29 X X Y Y-- 15 1 7-3.250 5.125 10.563 26.266-16.656 17 1 3-1.250 1.125 1.563 1.266-1.406 25 5 6.750-6.875 45.563 47.266-46.406 27 7 8.750-4.875 76.563 23.766-42.656 17 7-1.250-4.875 1.563 23.766 6.094 12 2 1-6.250 9.125 39.063 83.266-57.031 11 1 9-7.250 7.125 52.563 50.766-51.656 22 6 3.750-5.875 14.063 34.516-22.031 6.6....
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  • Spring '08
  • HALEY
  • Correlation and dependence, Pearson product-moment correlation coefficient, Covariance and correlation, Spearman's rank correlation coefficient, Reject Ho

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Chap013 - C HAPTER 13 L INEAR R EGRESSION AND C ORRELATION...

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