Answer: let x 1 x, x 2 x^2 ,andlet
The least-square estimate for is given by Equation (11.49), with
and
Thus
or
Table 11. 5 Population increase, y, with
number of years after 1970, x, for Example 11.7
x 012345
y(%) 1.03 1.32 1.57 1.75 1.83 2.33
358 Fundamentals of Probability and Statistics for Engineers
q
(^0)
(^1)
(^2)
2
4
3
(^5) :
q,^q,
C
10 0
11 1
12 4
13 9
1416
1525
2
6
6
6
6
(^66)
4
3
7
7
7
7
(^77)
5
y
1 : 03
1 : 32
1 : 57
1 : 75
1 : 83
2 : 33
2 6 6 6 6 6 6 4
3 7 7 7 7 7 7 5
^q
CTC^1 CTy
61555
15 55 225
55 225 979
2
6
4
3
7
5
(^19) : 83
28 : 68
110 : 88
2
6
4
3
7
5
1 : 07
0 : 20
0 : 01
2
6
4
3
7
5 ;
^ 0 1 : 07 ; ^ 1 0 : 20 ; and ^ 2 0 : 01 :