nfl x1 x2 x3 x4 x5 x6 x7 88 x8 x9 99 10 2113 1985 38.9 64.7 4 868 59.7 2205 1917 11 2003 2855 38.8 61.3 3 615 55 2096 1575 11 2957 1737 40.1 60 14 914 65.6 1847 2175 13 2285 2905 41.6 45.3 -4 957 61.4 1903 2476 10 2971 1666 39.2 53.8 15 836 66.1 1457 1866 11 2309 2927 39.7 74.1 8 786 61 1848 2339 10 2528 2341 38.1 65.4 12 -1 754 66.1 1564 2092 11 2147 2737 4 1689 1414 42.1 47.6 -3 783 57 2577 2001 2 2566 1838 42.3 54.2 -1 797 58.9 2476 2254 13 58 1821 1909 7 2363 1480 37.3 8 19 984 67.5 1984 2217 10 2109 2191 39.5 51.9 6 700 57.2 1917 1758 9 2295 2229 37.4 53.6 -5 1037 58.8 1761 2032 9 1932 2204 35.1 71.4 3 986 58.6 1709 2025 6 2213 2140 38.8 58.3 60 819 59.2 1901 1686 5 1722 1730 36.6 52.6 -19 791 54.4 2288 1835 5 1498 2072 35.3 59.3 072 35.3 59.3 -5 776 49.6 2072 1914 5 1873 2929 41.1 55.3 10 789 54.3 2861 2496 6 2118 2268 38.2 69.6 6 582 58.7 2411 2670 4 1775 1983 39.3 78.3 7 901 51.7 2289 2202 3 1904 1792 39.7 38.1 -9 734 61.9 2203 1988 3 1929 1606 39.7 68.8 -21 627 52.7 2592 2324 4 2080 1492 35.5 68.8 -8 722 57.8 2053 2550 10 2301 2835 35.3 74.1 2 683 59.7 1979 2110 6 2040 2416 38.7 50 0 576 54.9 2048 2628 8 2447 1638 39.9 57.1 -8 848 65.3 1786 1776 2 1416 2649 37.4 56.3 -22 684 43.8 2876 2524 37 0 1503 1503 39.3 47 -9 875 53.5 2560 2241 Question 1 nfl.csv gives data concerning the performance of the 28 National Football League teams in 1976. It is suspected that the number of passing yards gained by opponents (x9) has an effect on the number of games won by a team (y). NOTE: for this question, you are expected to use R to perform the analysis. You don't need to submit the R program and outputs. You can adopt the numbers directly from the computer output for the analysis. (a) Plot x9 versus y. Does the plot suggest that y and x9 are linearly associated? (b) Fit a simple linear regression model relating games won y to passing yards gained by opponents x9. Report the fitted regression line. (c) Construct the analysis-of-variance table. (d) Test for the significance of regression at the 5% level of significance. (e) Find a 90% confidence interval on the slope. (f) What percent of the total variability in y is explained by this model? (g) Find a 90% confidence interval on the mean number of games won if opponents' passing yards rushing is limited to 2000 yards. (h) Find a 90% prediction interval on the number of games won if opponents' passing yards rushing is limited to 2000 yards.