Fundamentals of Probability and Statistics for Engineers

(John Hannent) #1
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


ˆˆ


(^0)
(^1)
(^2)


2

4

3

(^5) :
q,^q,



10 0

11 1

12 4

13 9

1416

1525

2

6

6

6

6

(^66)
4


3

7

7

7

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(^77)
5


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

^qˆ…CTC†^1 CTyˆ

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15 55 225

55 225 979

2

6

4

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 (^19) : 83
28 : 68
110 : 88


2

6

4

3

7

5

ˆ

1 : 07

0 : 20

0 : 01

2

6

4

3

7

5 ;

^ 0 ˆ 1 : 07 ; ^ 1 ˆ 0 : 20 ; and ^ 2 ˆ 0 : 01 :
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