Consider the National Football League data in Table B.1. a. Fit a multiple linear regression model...

   

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Consider the National Football League data in Table B.1. a. Fit a multiple linear regression model relating the number of games won to the team's passing yardage (x₂), the percentage of rushing plays (x7), and the opponents' yards rushing (xs). b. Construct the analysis-of-variance table and test for significance of regression. c. Calculate t statistics for testing the hypotheses Ho: B₂ = 0, Ho: B₁ = 0, and Ho: Ps= = 0. What conclusions can you draw about the roles the variables x2, X7, and xs play in the model? d. Calculate R² and Råd for this model. Adj e. Using the partial F test, determine the contribution of x7 to the model. How is this partial F statistic related to the t test for B, calculated in part c above? TABLE B.1 National Football League 1976 Team Performance Team y X1 X3 X₂ Washington 10 2113 Minnesota 11 2003 New 1985 38.9 2855 38.8 64.7 61.3 60.0 +14 X4 Xs X6 X7 X8 +4 868 59.7 2205 1917 +3 615 55.0 2096 1575 11 2957 1737 40.1 914 65.6 1847 2175 England Oakland 13 2285 2905 41.6 45.3 -4 957 61.4 1903 2476 Pittsburgh 10 2971 1666 39.2 53.8 +15 836 66.1 1457 1866 Baltimore 11 2309 2927 39.7 74.1 +8 786 61.0 1848 2339 Los Angeles 10 2528 2341 38.1 65.4 +12 754 66.1 1564 2092 Dallas 11 2147 2737 37.0 78.3 -1 761 58.0 1821 1909 Atlanta 4 1689 1414 42.1 47.6 714 57.0 2577 2001 Buffalo 2 2566 1838 42.3 54.2 -1 797 58.9 2476 2254 Chicago 7 2363 1480 37.3 48.0 984 67.5 1984 2217 Cincinnati 10 2109 2191 39.5 51.9 700 57.2 1917 1758 Cleveland 9 2295 2229 37.4 53.6 1037 58.8 1761 2032 Denver 9 1932 2204 35.1 71.4 986 58.6 1709 2025 Detroit 6 2213 2140 38.8 58.3 819 59.2 1901 1686 5 1722 1730 36.6 52.6 -19 791 54.4 2288 1835 Green Bay Houston Kansas City 5 1498 2072 35.3 59.3 776 49.6 2072 1914 5 1873 2929 41.1 55.3 789 54.3 2861 2496 6 2118 2268 38.2 69.6 582 58.7 2411 2670 Miami New 4 1775 1983 39.3 78.3 901 51.7 2289 2202 Orleans 3 1904 1792 39.7 38.1 -9 734 61.9 2203 1988 New York Giants New York 3 1929 1606 39.7 68.8 -21 627 52.7 2592 2324 2080 68.8 -8 57.8 2053 2550 Jets Philadelphia St. Louis San Diego San 1492 35.5 2835 35.3 722 683 59.7 10 2301 74.1 +2 1979 2110 2040 2416 38.7 50.0 0 576 54.9 2048 2628 8 2447 1638 39.9 57.1 -8 848 65.3 1786 1776 Francisco Seattle 2 1416 37.4 56.3 -22 43.8 2876 2524 2649 1503 39.3 47.0 684 -9 875 53.5 Tampa Bay 0 1503 2560 2241 y: Games won (per 14-game season) 1₁: Rushing yards (season) X₂: Passing yards (season) x: Punting average (yards/punt) x: Field goal percentage (FGs made/FGs attempted 2season) Xs: Turnover differential (turnovers acquired-turnovers lost) x: Penalty yards (season) x: Percent rushing (rushing plays/total plays) x₂: Opponents' rushing yards (season) X: Opponents' passing yards (season) 4066 7477487345 +19 +6 -5 +3 +6 -5 +10 +6 Consider the National Football League data in Table B.1. a. Fit a multiple linear regression model relating the number of games won to the team's passing yardage (x₂), the percentage of rushing plays (x7), and the opponents' yards rushing (xs). b. Construct the analysis-of-variance table and test for significance of regression. c. Calculate t statistics for testing the hypotheses Ho: B₂ = 0, Ho: B₁ = 0, and Ho: Ps= = 0. What conclusions can you draw about the roles the variables x2, X7, and xs play in the model? d. Calculate R² and Råd for this model. Adj e. Using the partial F test, determine the contribution of x7 to the model. How is this partial F statistic related to the t test for B, calculated in part c above? TABLE B.1 National Football League 1976 Team Performance Team y X1 X3 X₂ Washington 10 2113 Minnesota 11 2003 New 1985 38.9 2855 38.8 64.7 61.3 60.0 +14 X4 Xs X6 X7 X8 +4 868 59.7 2205 1917 +3 615 55.0 2096 1575 11 2957 1737 40.1 914 65.6 1847 2175 England Oakland 13 2285 2905 41.6 45.3 -4 957 61.4 1903 2476 Pittsburgh 10 2971 1666 39.2 53.8 +15 836 66.1 1457 1866 Baltimore 11 2309 2927 39.7 74.1 +8 786 61.0 1848 2339 Los Angeles 10 2528 2341 38.1 65.4 +12 754 66.1 1564 2092 Dallas 11 2147 2737 37.0 78.3 -1 761 58.0 1821 1909 Atlanta 4 1689 1414 42.1 47.6 714 57.0 2577 2001 Buffalo 2 2566 1838 42.3 54.2 -1 797 58.9 2476 2254 Chicago 7 2363 1480 37.3 48.0 984 67.5 1984 2217 Cincinnati 10 2109 2191 39.5 51.9 700 57.2 1917 1758 Cleveland 9 2295 2229 37.4 53.6 1037 58.8 1761 2032 Denver 9 1932 2204 35.1 71.4 986 58.6 1709 2025 Detroit 6 2213 2140 38.8 58.3 819 59.2 1901 1686 5 1722 1730 36.6 52.6 -19 791 54.4 2288 1835 Green Bay Houston Kansas City 5 1498 2072 35.3 59.3 776 49.6 2072 1914 5 1873 2929 41.1 55.3 789 54.3 2861 2496 6 2118 2268 38.2 69.6 582 58.7 2411 2670 Miami New 4 1775 1983 39.3 78.3 901 51.7 2289 2202 Orleans 3 1904 1792 39.7 38.1 -9 734 61.9 2203 1988 New York Giants New York 3 1929 1606 39.7 68.8 -21 627 52.7 2592 2324 2080 68.8 -8 57.8 2053 2550 Jets Philadelphia St. Louis San Diego San 1492 35.5 2835 35.3 722 683 59.7 10 2301 74.1 +2 1979 2110 2040 2416 38.7 50.0 0 576 54.9 2048 2628 8 2447 1638 39.9 57.1 -8 848 65.3 1786 1776 Francisco Seattle 2 1416 37.4 56.3 -22 43.8 2876 2524 2649 1503 39.3 47.0 684 -9 875 53.5 Tampa Bay 0 1503 2560 2241 y: Games won (per 14-game season) 1₁: Rushing yards (season) X₂: Passing yards (season) x: Punting average (yards/punt) x: Field goal percentage (FGs made/FGs attempted 2season) Xs: Turnover differential (turnovers acquired-turnovers lost) x: Penalty yards (season) x: Percent rushing (rushing plays/total plays) x₂: Opponents' rushing yards (season) X: Opponents' passing yards (season) 4066 7477487345 +19 +6 -5 +3 +6 -5 +10 +6

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Here Used Excel and solve Here y Is response variable and x2x7 and x8 is pre... View the full answer