Suppose we would like to use the model developed in Problem 2.1 to predict the number of games a team will win if it can limit opponents' yards rushing to 1800 yards. Find a point estimate of the number of games won when $x_{8}=1800$. Find a $90 %$ prediction interval on the number of games won.

Data From Problem 2.1

Table B. 1 gives data concerning the performance of the 26 National Football League teams in 1976. It is suspected that the number of yards gained rushing by opponents $\left(x_{8}\right)$ has an effect on the number of games won by a team $(y)$.

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Team Washington y x1 10 2113 X2 X3 X4 X5 X6 X7 xx X9 1985 38.9 64.7 Minnesota 11 2003 2855 38.8 61.3 +3 615 New 11 2957 1737 40.1 60.0 +14 England Oakland 13 2285 2905 41.6 45.3 Pittsburgh 10 2971 1666 39.2 53.8 +15 Baltimore 11 2309 2927 39.7 74.1 Los Angeles 10 2528 2341 38.1 65.4 Dallas 11 2147 2737 370 78.3 1977 +4 868 59.7 2205 1917 55.0 2096 1575 914 65.6 1847 2175 -4 957 61.4 1903 2476 836 +8 +12 -1 Atlanta 4 1689 1414 42.1 476 -3 714 Buffalo 2 2566 1838 42.3 54.2 -1 66.1 1457 1866 786 61.0. 1848 2339 754 66.1 1564 2092 761 58.0 1821 1909 570 797 58.9 2577 2001 2476 2254 Chicago 7 2363 1480 373 48.0 +19 Cincinnati 10 2109 2191 39.5 51.9 Cleveland 9 2295 2229 374 53.6 Denver 9 1932 2204 35.1 71.4 Detroit 6 2213 2140 38.8 58.3 Green Bay 5 1722 1730 36.6 52.6 Houston 5 1498 2072 35.3 59.3 Kansas City 5 1873 2929 41.1 55.3 Miami 6 2118 2268 38.2 69.6 New 4 1775 1983 39.3 78.3 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 39.9 571 Francisco Scattle Tampa Bay 20 1416 2649 374 56.3 1503 1503 39.3 470 479497447 9789 +6 -5 984 675 700 572 1037 58.8 1984 2217 1917 1758 1761 2032 +3 986 58.6 1709 2025 -19 +6 819 791 54.4 59.2 1901 1686 2288 1835 -5 776 49.6 2072 1914 +10 789 54.3 2861 2496 +6 582 58.7 2411 2670 +7 901 51.7 2289 2202 -9 734 61.9 2203 1988 -21 627 52.7 2592 2324 -8 722 578 2053 2550 +2 683 59.7 1979 2110 0 -8 848 576 54.9 65.3 2048 1786 1776 2628 -22 684 43.8 2876 2524 -9 875 53.5 2560 2241