HW # 14, 1 December

Homework # 14
due 1 December
The index of biotic integrity (IBI) is a measure of the water quality in streams. IBI and land-use
measures for a collection of streams in the Ozark Highland ecoregion of Arkansas were collected
as part of a study. The IBI data set (next page) gives data for the 49 streams in the original sample
with area less than or equal to 70 km2. The variables are the area of the watershed (in square
kilometers), the IBI, and the percent of the area that was forested.
For the following, treat IBI as the response variable.
(1) Use numerical and graphical methods to describe the variable IBI. Do the same for area.
Summarize your results.
(2) Plot the data and describe the relationship between IBI and area. Are there any outliers or
unusual patterns?
(3) (a) State the statistical model (not the estimates of the model) for simple linear regression for
the relationship between IBI and area (with IBI as the response variable).
(b) State the null and alternative hypotheses for examining the relationship between IBI and
area.
(c) Run the simple linear regression and summarize the results.
(4) (a) Find a 95% confidence interval for mean response corresponding to an area of 30 km2.
(b) Find a 95% prediction interval for a future response in an area of 30 km2.
(c) Write a short paragraph interpreting the meaning of these intervals in terms of Ozark
Highland streams.
(d) Do you think that these results can be applied to other streams in Arkansas or in other
states? Explain why or why not.
Area
21
29
31
32
34
34
49
52
2
70
6
28
21
59
69
47
8
8
58
54
10
57
18
19
39
IBI Forest
47
0
61
0
39
0
59
0
72
0
76
0
85
3
89
3
74
7
89
8
33
9
46
10
32
10
80
11
80
14
78
17
53
17
43
18
88
21
84
22
62
25
55
31
29
32
29
33
54
33
Area
49
9
5
14
9
23
31
18
16
21
32
10
26
9
54
12
21
27
23
26
16
26
26
28
IBI Forest
78
33
71
39
55
41
58
43
71
43
33
47
59
49
81
49
71
52
75
52
64
59
41
63
82
68
60
75
84
79
83
79
82
80
82
86
86
89
79
90
67
95
56
95
85
100
91
100

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