Least Square Method
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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