Please give the solution of the following programs in R Programming
- by NEETHU
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.
Consider the Oxygen plant data in Problem3 and assume that purity and Hydrocarbon percentage are jointly normally distributed r.vs
(a)What is the correlation between Oxygen purity and Hydrocarbon%
(b)Test the hypothesis that ?=0.
(c)Construct a 95% CI for ?.
