Geoscience Reference
In-Depth Information
0.8
0.6
0.4
0.2
0
20
40
60
80
100
X = Crown Volume
FIGURE 7.3
Plotting of growth ( F ) over crown volume ( X ).
The type of pattern (straight line, parabolic curve, exponential curve, etc.) will influence the
regression model to be fitted. In this particular case, we will assume a simple straight-line relation-
ship. After selecting the model to be fitted, the next step will be to calculate the corrected sums of
squares and products. In the following equations, capital letters indicate uncorrected values of the
variables; lowercase letters will be used for the corrected values.
The corrected sum of squares for Y is
2
n
∑∑
n
Y
n
2
26
62
62
(
)
2
2
2
2
2
y
=
Y
=
036009
.
+ ++
.
042
.
=
2 7826
.
The corrected sum of squares for X is
2
n
∑∑
n
X
n
2
3050
62
(
)
2
2
2
2
2
x
=
X
=
22
+ ++
6
61
=
5
9 397 6775
,
.
The corrected sum of products is
n n
∑∑ ∑∑
=
n
XY
n
(
3050 26 62
62
)(.
)
[
]
xy
=
(
XY
)
( (. )()(
22
03660..
+
09
)
++
(
61 042
)( .)
=
354 14
.
77
The general form of equation for a straight line is Y = a + bX . In this equation, a and b are constants
or regression coefficients that must be estimated. According to the principle of least squares, the
best estimates of these coefficients are
2
xy
x
354 1477
59 397 6775
.
b
=
=
=
0 005962
.
,
.
aY bX
=− =
0 42935
.
( .
0 005962
)(.
49 1935
)
=
0 13606
.
 
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