Geoscience Reference
In-Depth Information
(
)
+
(
)
+
(
)
+
…
+
(
)
equation:
∑∑ ∑
∑∑
2
b
x
b
x xb
xx b
xx
b
=
x y
1
1
1
1
22
13
3
1
kk
1
(
)
+
(
)
+
(
)
++
(
)
∑
∑
∑
∑
∑
2
b
equation:
x xb
x
b
x xb
…
xx b
=
x y
2
1
21
2
2
2
33
2
kk
2
(
)
+
(
)
+
(
)
++
(
)
∑
∑
∑
∑
∑
2
b
equation:
xx b
x xb
xb
…
xx
kk
=
xy
3
13
1
2
32
3
3
3
3
(
)
+
(
)
(
)
++
(
)
∑
∑
∑
∑
∑
2
b
equation:
x xb
xx b
+
x x
b
…
x
b
=
x y
k
1
k
1
2
k
2
3
k
3
k
k
k
Given the
X
coefficients, the constant term can be computed as
aY bX
=− −
bX
22
…
−
−
b
kk
11
Note that the normal equations for the general linear model include the solution for the simple linear
regression
(
)
=
∑∑
2
xb
xy
1
1
1
Hence,
=
(
∑∑
2
b
x y
x
1
1
1
In fact, all of this section on multiple regression can be applied to the simple linear regression as a
special case.
The corrected sums of squares and products are computed in the familiar manner:
−
(
)
=++
2
∑∑
∑
Y
n
2
(
2206
28
)
(
)
−
2
2
2
2
y
=
Y
65
…
61
=
5974 7
. 143
−
(
)
=++
2
∑∑
∑
X
n
2
(
1987
28
)
(
)
−
1
2
2
2
2
x
=
X
41
…
46
=
11 436 9643
,
.
1
1
−
(
)(
)
=
∑∑
∑∑
XY
n
( ()
(
1987 2206
28
)(
)
1
xy
=
XY
( ()
41 65
+
…
+
46
61
−
=
6428 7858
.
1
1
Similarly,
∑
∑
∑
xx
=−
1171 4642
.
12
xx
=
3458 8215
.
13
2
x
=
5998 96
.43
2
∑
∑
∑
xx
=
1789 6786
.
23
xy
=
2632 2143
.
2
2
x
=
2606 1
.072
x
∑
=
3327 9286
.
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