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Determinacion minimos cuadrados

  • 1. ! " # $ % " & ' ' " ' ( % " ) * + , - . /* 0 + *- + /1 , , , - , 0+= = = = = = ) 0 1 2 3 4 5 0 1 2 3 4 5 6 7 2 & ' & ' 3 ! & ' ( & ' 3 % 4 ' & % 3 ' & 5 ( 3 % 3
  • 2. % ( % 3 ! % ) % % " % % 6 3 % 7 8 ' & ( 2 6 2 % ) x x x x x x x x x X Y x " & ' & ' ! ) 9 : ; "
  • 3. 3 ) x x x x x x x x x y=ax+b e y' x y'+e " < ) ′ = + ! ) = − ′ % ) != ′+ = + + ( % % % 7 8 ! 3 ! ! ! ) "# " = * ! = − 3% )= 1- % ' % & & ' 3 2 )
  • 4. $ " % > * 1 ? - ,- 01 * 1* - .@ 1,, + . 1 . +. , ? , +. 01 - / * 1, ,? . ? * 10 01 / - 1 - *- 0 ? + */ 01 ? / + *1 ,? 1@ + 1 + ? 11 1@ , ,@ 1@@ 1* . * 1* +. 1+ 11 - -- 1*1 1, , * 0 1. 1- 1+ - .- 1.? A 1*@ ,- ,1- 1@/0 2 ' 1*@B1- 9 0 2 & ,-B1- 9 + 2 ,1-B1- C *, 9 + ./ 2 ' 1@/0B1- C ., 9 / 0/ ( ) 9 + ./B/ 0/ 9 @ ,.. ) 9 + C @ ,..>0 9 + C + /*0 9 C@ /*0 & ' ) 9 @ ,.. C @ /*0 D % % 4 & ') ′ = + ! & 3 ( % 6 % )
  • 5. <9 @ ,.. C @ /*0 0 ) <9 @ ,..>0 C @ /*0 9 + % 0 % 0 A! ) 9 : : ! 6 ( % ? 1E,E.E 0E ) <9 @ ,..>? C @ /*0 9 + ,.. 1 9 - , 9 , . 9 * 0 9 + ) 1 9 - C + ,.. 9 1 -+,F , 9 , C + ,.. 9 @ -+,F . 9 * C + ,.. 9 C1 ,.. 0 9 + C + ,.. 9 C@ ,.. D < 6 < & ) 9 <: & ) # * * * = +′ 2 & ' G & ' ( ) # % * *
  • 6. & % " ) <9 : ' " G 6 ( 3 ) "% * * * = ) "# " "# " " "# " = = ⋅ =* * * , * * *% & ) # "# " # % * * * * * * = = ( & & ' 5 & ' ' & ' & )
  • 7. ' * * * * * * * * * x=a'y+b' e x y x' & ' & H ' & ! ; ! ) ′ = − ′! ′ = "# # * 3% )" ' & ) 2 ' 0 / 0/ 2 & + * */ 2 + ./ ( + ./B* */ 9 1 .1/ 0 C 1 .1/>+ 9 + 1,? 2 ) 9 1 .1/ : + 1,? " )
  • 8. ( @ 1 * + , - . , 0 1* 9 @ ,.. C@ /*0 91 .1/ :+ 1,? ! " 4 3 ) ( )[ ]) != = − + = = * 1 * 1 ( ( ) ( )[ ] ( ) ∂ ∂ ) ! != ⋅ − + ⋅ − = * 1 1 ) ( )[ ]( ) ( )[ ]( )* 1 @ 1 @ 1 1 ! !− + − = − + − = = = ) − + + = + = === == = ! !@ 111 11 1 6 ) !+ = = =1 1 4 ) ( )[ ] ( )∂ ∂ ) != ⋅ − + ⋅ − = * 1 )
  • 9. * ( )[ ]( ) ( )[ ]( )* @ @ 1 1 ! !− + − = − + − = = = ) − + + = + = === == = ! !* 111 * 11 1 @ 6 ) !* 11 1 + = == = 4 % ) ! ! !+ = = − = − = = = = = = 1 1 1 1 1 1 ) ! = − " ! ) ! !* 11 1 * 1 1 1 + = + = == = = = = ) ( ) * 1 1 * 1 * 1= = = = + − = + ⋅ − = 6 ! ) " "# * 1 * 1 *= = − = − ⋅ = ) "# " = *