The Method of Least Squares - Elements of Scientific Computing - page 160

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. 5.10 Constant, linear and quadratic approximations of global annual mean temperature devi-
ation measurements (relative to the 1961-1990 mean), year 1991 to 2000

Using, e.g., Matlab, we find that the solution of this linear system is given by

˛ 0:4078;
ˇ 0:2997; (5.43)

0:0241:

So far, we have not discussed how to solve linear systems. Let us, for the time
being, just accept that such a system can be solved under proper conditions on the
matrix of the system. We will return to this topic in later chapters. In Fig. 5.10 ,we
have plotted the data given in Table 5.1 together with the constant approximation

p 0 .t / D 0:312; (5.44)

the linear approximation

p 1 .t / D 0:123 C 0:034t; (5.45)

and the quadratic approximation

p 2 .t / D 0:4078 C 0:2997t 0:0241t 2 :

(5.46)