Information Technology Reference
In-Depth Information
For a given set of data .t
i
;y
i
/, the linear system (
5.65
) can be solved using, e.g.,
Matlab.
Application to the Temperature Data
We will now use the methods derived above to model the data describing the change
in the global temperature from 1856 to 2000.
3
Based on the data, we need to compute the entries in (
5.52
), (
5.58
)and(
5.65
):
14
X
14
X
t
i
n
D
145;
t
i
D
10585;
D
1026745;
i D1
i D1
14
X
14
X
14
X
t
i
D
1:12042
10
8
;
t
i
D
1:30415
10
10
;
y
i
D
21:82;
(5.66)
i D1
i D1
i D1
X
145
X
145
t
i
t
i
y
i
D
502:43;
y
i
D
19649:8;
i D1
i D1
wherewehaveusedt
i
D
i , i.e., t
1
D
1 corresponds to the year of 1856, t
2
D
2
corresponds to the year of 1857, and so forth.
From (
5.48
)and(
5.52
), we now have
p
0
.t /
0:1505:
(5.67)
The coefficients ˛ and ˇ of the linear model (
5.53
) are obtained by solving the
linear system (
5.58
), i.e.,
145 10585
10585 1026745
˛
ˇ
D
21:82
502:43
:
(5.68)
Consequently,
˛
0:4638
and
ˇ
0:0043;
so the linear model is given by
p
1
.t /
0:4638
C
0:0043 t:
(5.69)
Similarly, the coefficients ˛, ˇ and of the quadratic model (
5.59
) are obtained
by solving the linear system (
5.65
), i.e.,
3
See
http://cdiac.ornl.gov/ftp/trends/temp/jonescru/global.dat
.
