Points/Games Ratio (y) Estimate (for questions 9 to 12) 9. The residual standard deviation, . c) 0.062 d) 0.085 h) 0.143 i) 0.236 e) 0.091 j) 0.266 Choices a) 0.045 b) 0.058 f) 0.132 g) 0.136 10. The slope of the regression line, , with a 95% confidence interval. 11. The slope of the regression line, , with a 99% confidence interval. 12. The intercept of the regression line, , with a 95% confidence interval. Choices for 10 to 12. a) 0.411 to 1.013 b) 0.063 to 0.694 d) -0.04 to 0.797 e) 0.153 to 0.605 c) 0.079 to 0.679 f) 0.496 to 0.928 Predict (for questions 13 to 15) 13. The y (Pts/Games ratio) for a team with x = GF/GA ratio = 1.14 with a 95% prediction interval. 14. The y (Pts/Games ratio) for a team with x = GF/GA ratio = 1.14 with a 99% prediction interval. 15. The y (Pts/Games ratio) for a team with x = GF/GA ratio = 0.81 with a 95% prediction interval. Choices for 13 to 15. a) 0.887 to 1.024 b) 0.985 to 1.396 e) 0.860 to 1.051 f) 1.133 to 1.248 c) 0.904 to 1.477 g) 0.664 to 1.247 d) 1.111 to 1.270 h) 0.747 to 1.164 16. Identify the x-y scatter plot of the data Choices Points/Games Ratio (y) a) b) 1.2 1 1.6 0.8 0.6 0.4 Points/Games Ratio (y) 1.4 1.2 1 0.8 0.6 0.4 0.2 0.2 0 0 0.00 0.20 0.40 0.60 0.80 1.00 0.00 0.50 GF/GA ratio (x) 1.00 GF/GA ratio (x) 1.50 2.00 1.4 c) 1.4 1.2 1 0.8 0.6 0.4 Points/Games Ratio (y) 1 0.6 0.4 0.2 0.2 0 0 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 0.00 0.20 0.40 0.60 GF/GA ratio (x) Page 2 d) 0.80 1.00 GF/GA ratio (x) 1.20 1.40 1.60 I. Below is a table showing team statistics for National Hockey League (NHL) Eastern Conference teams recorded on Dec 11, 2011, (Games = the number of games played, GF = the number of goals scored by the team, GA = the number of goals scored against the team, Pts = the number of points earned by the team (2 points for a win, 0 points for a loss, 1 point for an OT loss), x = GF/GA ratio, y = Pts/Games = points earned per game. Eastern Conference NHL Statistics (Dec 11, 2011) Team Games Wins Losses OT losses GF GA Pts GF/GA (X Pts/Games (y) Philadelphia 28 18 NY Rangers 26 16 Boston 28 18 868 7 3 101 81 39 1.25 1.39 6 4 77 59 36 1.31 1.38 9 1 94 59 37 1.59 1.32 Florida 29 Pittsburgh Toronto 29 Washington 28 Buffalo New Jersey Montreal Winnipeg 22222222 16 8 5 81 71 37 1.14 1.28 30 17 9 4 94 75 38 1.25 1.27 15 11 3 91 94 33 0.97 1.14 15 12 1 88 89 31 0.99 1.11 29 15 12 2 79 79 32 1.00 1.10 28 14 13 1 71 80 29 0.89 1.04 30 12 11 7 74 77 31 0.96 1.03 29 13 12 4 82 92 30 0.89 1.03 Ottawa 30 13 13 4 91 105 30 0.87 1.00 Tampa Bay 29 12 15 2 NY Islanders 27 9 12 6 26 75 96 26 0.78 0.90 62 88 24 0.70 0.89 Carolina 31 9 18 4 79 108 22 0.73 0.71 Ex = 15.32 Ex = 16.4838 Suppose one is interested in predicting y (Pts/Games) from x (GF/GA). Compute (for questions 1. to 8.) = 16.59 = 18.8815 xy = 17.5399 1. Sxx 2. Syy 3. Sxy 4. The slope of the least squares line, b. 5. The intercept of the least squares line, a. 6. The Residual Sum of Squares (RSS). 7. Pearson's correlation coefficient, r, 8. The coefficient of determination. Choices for 1 to 8 a) 0.109 b) 0.329 c) 0.379 d) 0.533 f) 0.596 g) 0.712 h) 0.796 i) 0.837 e) 0.556 j) 0.892