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#!AT $S LEAST SQUAEMET!"D%

A mathematical procedure for nding the

best-tting equation to a given set ofpoints by minimizing the sum of thesquares of the osets (“residuals") of thepoints from the curve

Also used in!redicting the futurevalues of the curve

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F"MULAE

F&'mula &' h* E+, & *.&n*nial *+uai&n/  a-

F&' alu*s & a5 and 5

  A6nB68A62B668

#h*'*9  8l&:10

  Al&:10

  Bl&:10 a

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Q1,Find h* *+uai&n & ;u'<* ha *s =sh* &ll&>in: daa, Als& =nd (10),

# $ % & '

11 12 14 1? 1@ 21 23

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S&lui&n

y *+log,

y* .

3 11 1,0413@ 3,12417 @

4 12 1,07@1? 4,3172 1

14 1,1412 ,730 2

1? 1,227 7,312 3

7 1@ 1,27?7 ?,@12 4@

? 21 1,32221 10,77?

4

@ 23 1,3172 12,24?

?1

42 - ?,4?44 2,4?72

2?0

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Sin;*9  A6nB68

  A62B668

 Th*'*&'*9  42A 7B ?,4?4? -------(1)  2?0A 42B 2,4?72 -----(2)S&l<in: *+ 1 and 29 >* :*9  A0,041C B0,?73?

Al&:10 0,041C 1,13?70  Bl&:10 a0,?73?C a7,4744

 Th*'*&'*,  7,4744(1,13?70)

F&' <alu* (10)  7,4744(1,13?70)10

  27,3@10

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Q2, Find h* *+uai&n ha *s = h*;u'<*,

, % ' ,. 10 1 12 1 21

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S&lui&n

y *+log,

y*

.

1 10 1 1 1

1 1,171 ,??0 2

7 12 1,07@2 7,44 4@

@ 1 1,171 10,?4@ ?1

12 21 1,3222 1,?4 144

34 - ,73 3@,??2 300

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Sin;*9  A6nB68

  A62

B668 Th*'*&'*9  34A B ,73-------(1)  300A 34B 3@,??2 -----(2)S&l<in: *+ 1 and 29 >* :*9  A0,011C B1,07  Al&:10 0,011C

1,02  Bl&:10 a1,07C

a11,?? Th*'*&'*,  11,?? (1,02)

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 Than 8&u