Page 375 - Fundamentals of Probability and Statistics for Engineers

358 Fundamentals of Probability and Statistics for Engineers

Table 11.5 Population increase, y, with

number of years after 1970, x, for Example 11.7
x 0 1 2 3 4 5
y(%) 1.03 1.32 1.57 1.75 1.83 2.33
2
Answer: let x 1 ˆ x, x 2 ˆ x , and let
2 3
0
q ˆ 4 1 :
5
2
^
The least-square estimate for q, q, is given by Equation (11.49), with
2 3
1 0 0
1 1 1
6 7
6 7
1 2 4
6 7
C ˆ 6 7
1 3 9
6 7
6 7
4 1 4 16 5
1 5 25
and
1:03
2 3
1:32
6 7
6 7
1:57
6 7
y ˆ 6 7
1:75
6 7
6 7
1:83
4 5
2:33
Thus
6 15 55 9:83
2 3 1 2 3
^ T 1 T 6 7 6 7
q ˆ C C† C y ˆ 4 15 55 225 5 4 28:68 5
55 225 979 110:88
1:07
2 3
0:20 5;
6 7
ˆ 4
0:01
or
^
^
^
0 ˆ 1:07; 1 ˆ 0:20; and 2 ˆ 0:01:

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