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In-Depth Information
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
Fig. 5.8
Two constant approximations of the global annual mean temperature deviation measure-
ments (relative to the 1961-1990 mean); from year 1991 to 2000
p.t/
D
˛
C
ˇt
(5.12)
fits the data as well as possible in the sense of least squares. Let us define
1
X
y
i
/
2
:
F.˛;ˇ/
D
.˛
C
ˇt
i
(5.13)
i D1
We want to minimize F with respect to ˛ and ˇ. A necessary condition for a
minimum is
@F
@˛
@F
@ˇ
D
D
0:
(5.14)
Since
1
X
@F
@˛
D
2
.˛
C
ˇt
i
y
i
/;
(5.15)
i D1
the condition
@F
@˛
D
0
(5.16)
