Table below gives data concerning the performance of 28 national football league teams in 1976.It is suspected that the no. of yards gained rushing by opponents(x8) has an effect on the no. of games won by a team(y) (a)Fit a simple linear regression model relating games won by y to yards gained rushing by opponents x8. (b)Construct the analysis of variance table and test for significance of regression. (c)Find a 95% CI on the slope. (d)What percent of the total variability in y is explained by this model. (e)Find a 95% CI on the mean number of games won in opponents yards rushing is limited to 2000 yards.
Team y x8 1 10 2205 2 11 2096 3 11 1847 4 13 1803 5 10 1457 6 11 1848 7 10 1564 8 11 1821 9 4 2577 10 2 2476 11 7 1984 12 10 1917 13 9 1761 14 9 1709 15 6 1901 16 5 2288 17 5 2072 18 5 2861 19 6 2411 20 4 2289 21 3 2203 22 3 2592 23 4 2053 24 10 1979 25 6 2048 26 8 1786 27 2 2876 28 0 2560

Suppose we would like to use the model developed in problem 1 to predict the no. of games a team will win if it can limit opponents yards rushing to 1800 yards. Find a point estimate of the no. of games won when x8=1800.Find a 905 prediction interval on the no. of games won.

The purity of Oxygen produced by a fractionation process is thought to be percentage of Hydrocarbon in the main condenser of the processing unit .20 samples are shown below. Purity(%) Hydrocarbon(%) 86.91 1.02 89.85 1.11 90.28 1.43 86.34 1.11 92.58 1.01 87.33 0.95 86.29 1.11 91.86 0.87 95.61 1.43 89.86 1.02 96.73 1.46 99.42 1.55 98.66 1.55 96.07 1.55 93.65 1.4 87.31 1.15 95 1.01 96.85 0.99 85.2 0.95 90.56 0.98

(a)Fit a simple linear regression model to the data. (b)Test the hypothesis H0:ß=0 (c)Calculate R2 . (d)Find a 95% CI on the slope. (e)Find a 95% CI on the mean purity and the Hydrocarbon % is 1.