Geoscience Reference
In-Depth Information
7.17
REGRESSION
7.17.1 s
imple
l
inear
r
egression
An environmental researcher had an idea that she could tell how well a loblolly pine was growing
from the volume of the crown. Very simple: big crown—good growth, small crown—poor growth.
But she couldn't say how big and how good, or how small and how poor. What she needed was
regression analysis, which would allow her to express a relationship between tree growth and crown
volume in an equation. Given a certain crown volume, she could use the equation to predict what
the tree growth was. To gather data, she ran parallel survey lines across a large tract that was rep-
resentative of the area in which she was interested. The lines were 5 chains apart. At each 2-chain
mark along the lines, she measured the nearest loblolly pine of at least 5.6 inches diameter at breast
height (d.b.h.; 4.5 ft above the forest floor on the uphill side of the tree) for crown volume and basal
area growth over the past 10 years.
A portion of the data is printed below to illustrate the methods of calculation. Crown volume in
hundreds of cubic feet is labeled
X
and basal area growth in square feet is labeled
Y
. Now, what can
we tell the environmental researcher about the relationship?
X
Crown
Volume
X
Crown
Volume
X
Crown
Volume
Y
Growth
Y
Growth
Y
Growth
22
0.36
53
0.47
51
0.41
6
0.09
70
0.55
75
0.66
93
0.67
5
0.07
6
0.18
62
0.44
90
0.69
20
0.21
84
0.72
46
0.42
36
0.29
14
0.24
36
0.39
50
0.56
52
0.33
14
0.09
9
0.13
69
0.61
60
0.54
2
0.10
104
0.66
103
0.74
21
0.18
100
0.80
43
0.64
17
0.17
41
0.47
22
0.50
87
0.63
85
0.60
75
0.39
97
0.66
90
0.51
29
0.30
33
0.18
27
0.14
76
0.61
20
0.06
18
0.32
20
0.29
96
0.58
48
0.21
29
0.38
61
0.42
37
0.54
30
0.53
67
0.70
59
0.58
56
0.67
70
0.62
31
0.42
81
0.66
17
0.39
93
0.69
7
0.25
99
0.71
2
0.06
14
0.14
Totals
3,050
26.62
Means (
n
= 62)
49.1935
0.42935
Often, the first step is to plot the field data on coordinate paper (see Figure 7.3). This is done to
provide some visual evidence of whether the two variables are related. If there is a simple relation-
ship, the plotted points will tend to form a pattern (a straight line or curve). If the relationship is very
strong, the pattern will generally be distinct. If the relationship is weak, the points will be more
spread out and the pattern less definite. If the points appear to fall pretty much at random, there may
be no simple relationship or one that is so very poor as to make it a waste of time to it any regression.
Search WWH ::
Custom Search