Use the regressors \(x_{2}\) (passing yardage), \(x_{7}\) (percentage of rushing plays), and \(x_{8}\) (opponents' yards rushing) for the National Football League data in Table B.1.

a. Does the correlation matrix give any indication of multicollinearity?
b. Calculate the variance inflation factors and the condition number of \(\mathbf{X}^{\prime} \mathbf{X}\). Is there any evidence of multicollinearity?

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Team y X X2 X3 X4 Washington 10 2113 1985 38.9 64.7 Minnesota 11 2003 2855 38.8 61.3 *77 X6 X7 Xg +4 868 59.7 2205 1917 +3 615 New 11 2957 1737 40.1 60.0 +14 914 55.0 2096 1575 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 370 78.3 -1 761 58.0 1821 1909 Atlanta 4 1689 1414 42.1 47.6 -3 714 570 2577 2001 Buffalo 2 2566 1838 42.3 54.2 -1 797 58.9 2476 2254 Chicago 7 2363 1480 373 48.0 +19 984 67.5 1984 2217 Cincinnati 10 2109 2191 39.5 51.9 +6 700 57.2 1917 1758 Cleveland 9 2295 2229 374 53.6 -5 1037 58.8 1761 2032 Denver Detroit Green Bay Houston Kansas City 96555 1932 2204 35.1 71.4 +3 986 58.6 1709 2025 2213 2140 38.8 58.3 +6 819 59.2 1901 1686 5 1722 1730 36.6 52.6 -19 791 54.4 2288 1835 1498 2072 35.3 59.3 -5 776 49.6 2072 1914 1873 2929 41.1 55.3 +10 789 54.3 2861 2496 Miami 6 2118 2268 38.2 69.6 New 4 1775 1983 39.3 78.3 47 +6 582 58.7 2411 2670 +7 901 51.7 2289 2202 Orleans New York 3 1904 1792 39.7 38.1 Giants New York 3 1929 1606 39.7 68.8 Jets Philadelphia 4 2080 1492 35.5 68.8 St. Louis 10 2301 2835 35.3 74.1 San Diego 6 2040 2416 38.7 50.0 San 8 2447 1638 39.9 57.1 Francisco Seattle 2 1416 2649 374 56.3 Tampa Bay 0 1503 1503 39.3 47.0 734 61.9 2203 1988 -21 627 52.7 2592 2324 722 57.8 2053 2550 683 0 -8 848 59.7 1979 576 54.9 2048 65.3 1786 1776 2110 2628 -22 684 43.8 2876 2524 875 53.5 2560 2241