Обработка данных / ElemTreat
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6
§ 6.1. % ($! & * (
& /! 8!*!4 '2! $ +!4!&- '$"*(&- 6 + &&-3! 81&25! - &(+,&-3! *($!'!3 '#"3!. ( !3 , *(2 & 3( $- (9( # +!& 0&1: *($!'!3 '#, # 2( $ 14('#2 5 ! # (6 &!" &( "9 &!" &( 7# 3 14('#- 2 . (2 & $' 3! & / #"/ # &!" 1#$ 96( #, 4# '!+( / ($!#(5!! -5! &(+,&( !*$ 6 &!: 3('' $*(!3 6 0'#$1:;!. # + ! ) (#&
5! &(+,&( 2$(6 (#1 (''# "&!" 3 961 &!3!. #! *($!'!3 '#! "$+":#'" ) ); &! 3 -#&-. 6(&&-. +!) +14(:#'" 3 # 6(3! # -#!4 '2 0 8!*!2!. !*!2! $' /6( '# 3"#'" !'(#, "$+ &!" ! - 5 ''- 81&25! &(+,&-3! *($!'!3 '#"3!.
6&(2 4('# &( &(4(+,& 3 7#( % &!" 2(2 0-+!) 8!*!4 '2 0)+ 3- $!6 81&25! &(+,& 0 '$"*! 3 961 6 + &&-3! 8!*!4 - '2!3! $ +!4!&(3! "$+" #'" & !*$ '#&-3. + # / , !& /6( '1; '#$1- :# ' 3& &!" $ &(+!4!! #(2 0 '$"*!. 2 # - 8!*!4 '2! $ +!4!&- 3 /1# )-#, & *($!'!3-3!.
''+ 6 $(&! !4!&& -'+ 6'#$ && 0 '$"*! 3 961 6$13" $ +!4!&(- 3! X ! Y $ 6!#'" 1# 3 !*3 &!0 *&(4 &!0 $ +!4!&- Y ! (*- +!4&-. *&(4 &!". $ +!4!&- X. +14 &&-3 *1+,#(#(3 6 +( #'"
$-$ 6 '$"*! !+! & *($!'!3 '#! 8!*!4 '2!. $ +!4!& X ! Y. + 61 # !3 #, $ $!61, 4# +:) 0 3 # 6 !*3 &!" $& '!# $ *1+,#(# & 2 # 1: '+14(0&1: / %& '#,, ( 7# , $ '$ : 4 6,, *(# 16&" # 6& *&(4&-0 $-$ 6 &(+!4!! 81&25! &(+,& 0 *($!'!3 '#! 3 961 6(&&-3! 8!*!4 - '2!3! $ +!4!&(3!.
! !*14 &!! (+,&-. 5 '' $ $-"'&" #'", 4# '1; '#$1:# 8!- *!4 '2! $ +!4!&-, 2 # - , ' 6& 0 '# &-, & '$"*(&- "$& 0 $*(!3- & 6& *&(4& 0 81&25! &(+,& 0 *($!'!3 '#,:, & , ' 6 1/ 0 '# &-,&! & "$+":#'" ! ()' +:#& & *($!'!3-3!. # *&(4!#, 4# ! 6& 3
! # 3 9 *&(4 &!! 3 && 0 X $ 72' !3 (. +14(:#'" (*+!4- &- *&(4 &!" 3 && 0 Y , !4 3 !. (*) ' *&(4!# +,& $-%(-# / %& '#, !*3 &!" Y. # 9 $ 3" ' 6&! *&(4 &!" Y - /1+" & 1$ +!4!$(:#'" !+! 13 &,%(:#'" ' '# 3 X. 6 )&- $ +!-
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4!&- &(*-$(:#'" , !+! / $ "#, 4# (''3(# !$( - 3(" ( ( $ +!4!& X ! Y '$"*(&( 3 961 ' ) 0 -
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# .('#!4 '2!3! *($!'!3 '#"3! '$"*(&- '+14(0&- $ +!4!&-, 2 -
# - $'# 4(:#'" 4#! $ $' . )+('#". 8!*!2!: # 3 6!&(3!2 , 2$( $ 0 8!*!2 , 3 .(&!2 3& /!. # +, # !! & +!& 0&-. 2 + )(&!0.# .('#!4 '2!3! *($!'!3 '#"3! !'-$(:#'" 3& /! )! 8!*!4 '2!5 ''-, 4# )1'+ $+ & '+ 9& '#,: !''+ 61 3-. )< 2# $.
!3 - (*+!4&-. $!6 $ $*(!3 '$"*! 3 &&-. $ +!4!& X ! Y!$ 6 &- $ $!6 / (8!2 $ &( !'. 4.
( (2#!2 *(4('#1: # 16& *1+,#(#(3 $ 6 &&-. !*3 - &!0 #+!4!#, «&( /+(*» '# /1: 81&25! &(+,&1: *($!'!3 '#, # '# -
.('#!4 '2 0 !*-*( ) +,% 0 $ +!4!&- '+14(0&-. / %& '# 0. #4 31 & ). 6!3 3(# 3(#!4 '2!0 3 # 6 (&(+!*( $*(!3 '$"*! -
3 &&-. X ! Y, 2 # -0 ! !*+(/( #'" $ 6(&& 0 /+($ .
Y Y Y
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!'. 4. (8!4 '2 6'#($+ &! *1+,#(# $ !*3 &!0 6+" (*&-. #! !4&-. '+14( $ $*(!3 '$"*! $ +!4!& X ! Y:
( − 81&25! &(+,& '$"*(&&- $ +!4!&- X ! Y, ) − '# .('#!4 '2! '$"*(&&- $ +!4!&- X ! Y,
$− & *($!'!3- $ +!4!&- X ! Y.
# 42! * &!" # !! $ "#& '# 0 2 +! $(&&- $ +!4!&- "$- +":#'" '+14(0&-3!. (*) ' *&(4 &!0 6& 0 $ +!4!&- ! '# "&'#$ *&(4 &!" 6 1/ 0 3 9 # )-#, !'(& ' 3 ;,: (' 6 + &!0 $ "#- & '# 0.
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§ 6.2. ' (-.. $ ( #$
'# 0% 0, & !&8 3(#!$& 0 .( (2# !'#!2 0 '$"*! 6$1. '+14(0- &-. $ +!4!& X ! Y "$+" #'" (-.. $ ( #$ . #( $ +!4!&(
6 +" #'" $ # !! $ "#& '# 0 ' 3 ;,: 6 1/!. $ "#& '#&-. 4!'+ $-. .( (2# !'#!2. 6(&& 3 ( (/ (8 3- / (&!4!3'" 4!'- + &! 3 '& $&-. '$ 0'#$ 2 788!5! ( 2 +"5!! ! ' ' ) $ ('4 - #(, )(*! 1:;!.'" &( 72' !3 (+,&-. *1+,#(#(.. :) *&(# +,&-3 4!#(# +"3 2 3 &61 #'" ) (#!#,'" 2 ' 5!(+,&-3 21 '(3 # !! $ -"#& '# 0 ('3. ' !' 2 2 3 &6 $(&& 0 +!# (#1 -).
!$ 6 3 # ! $(9& 0%!. '$ 0'#$( 2 788!5! ( 2 +"5!!, 2 # -- 6 2(*(&- $ # !! $ "#& '# 0.
1. ' /6( ρXY ≤ 1, #. . ()' +:#&(" $ +!4!&( 2 788!5! ( 2 - +"5!! & $-%( # 6!&!5-.
2.+" & *($!'!3-. $ +!4!& ρ XY = 0.
3.'+! $ +!4!&- X ! Y '$"*(&- 81&25! &(+,& 0 +!& 0& 0 *($!'!-
3 '#,: # |
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ρ XY |
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= 1. &(4 / $ ", '+! |
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ρ XY |
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= 1, # |
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Y = K X + B , |
(6.1) |
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/6 K ! B — & 2 # - '# "&&- .
788!5! 2 +"5!! "$+" #'" 16 )& 0 .( (2# !'#!2 0 $*(!- 3 '$"*! 6$1. 3 &&-. $ +!4!& X ! Y. 3 )+!9 2 &1+: $ +!4!&( ρ XY , # 3 ) +,% & /1+" &-0 (*) ' *&(4 &!0 $ +!4!&- Y ! +:- ) 3 8!2'! $(&& 3 *&(4 &!! X. ( #!$, '+! 2 788!5! ρ XY )+!* 2 2 6!&!5 , # *($!'!3 '#, Y(X) 3 9& !)+!9 && '4!#(#, +!& 0& 0.
3 # / , *&(2 2 788!5! ( 2 +"5!! 6& *&(4& 6 +" #
.( (2# *($!'!3 '#! Y(X). '+! ρ XY > 0, # $ +!4!&- X ! Y 6& - $ 3 && $ * ('#(:# !+! 1)-$(:# (' # 4& '#,: 6 '+14(0&-. / %-
& '# 0). '+! ρ XY < 0, # ' '# 3 X $ +!4!&( Y 1)-$( # !+! ' 13 &,- % &! 3 X $ +!4!&( Y ('# #.
(2!3 ) (* 3, 4!'+ && *&(4 &! 2 788!5! ( 2 +"5!! .(-(2# !*1 #, &('2 +,2 $*(!3 '$"*, 3 961 !''+ 61 3-3! $ +!4!&(3!
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X ! Y )+!*2( 2 *($!'!3 '#!. )' +:#&(" $ +!4!&( ρ XY )16 #
13 &,%(#,'" ! #2+ & &!! *($!'!3 '#! Y(X) # +!& 0& 0, 6(9 '+!
3 &&- '$"*(&- & '# .('#!4 '2!, ( '# / 81&25! &(+,& . + 6 - $(# +,& , !' +,* $(&! 2 788!5! ( 2 +"5!! 788 2#!$& 6+" !''+ 6 $(&!" #(2!. *($!'!3 '# 0, 4," )+!* '#, 2 +!& 0& 0 *( (&) '& $(&( # #!4 '2!.
+ ' ) (*& '#, !3 & &!" 2 788!5! ( 2 +"5!! '$"*(&( #(29 ' # 3, 4# $ $ 3 !)+!9 &!! 3& /! '+ 9&- *($!'!3 '#!+(/(:#'" +!& 0&-3!.
#!2 -$ "#& '#& 6 + &! 2 788!5! ( 2 +"5!! &!/ 6& 6+" (2#!4 '2!. $-4!'+ &!0. 2' !3 (# & !3 # $ '$ 3 (' "9 &!! # #!4 '21: !&8 3(5!: (' 6 + &!! $ -"#& '# 0 !''+ 61 3-. $ +!4!& ! '+14(0&-. / %& '# 0. 7# 31
$3 '# # 4& / *&(4 &!" 2 788!5! ( 2 +"5!! ρ XY |
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$-4!'+"#, / |
!)+!9 && *&(4 &! ( 5 &21), +,*1"', *1+,#(#(3! |
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!*3 &!0 $ +!4!& X ! Y. |
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1'#, $ 72' !3 )-+ |
$ 6 & N !*3 &!0 2(96 0 !* !*1- |
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4( 3-. $ +!4!& X ! Y ! +14 &- N ( 4!'+ $-. *&(4 &!0: |
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xi , yi |
; i = 1, … N . |
(6.2) |
(!+14%!3 |
!)+!9 &&-3 |
*&(4 &! 3 2 788!5! ( 2 +"5!!, |
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2 # 3 9& $-4!'+!#, ' 3 ;,: *1+,#(# $ !*3 &!0, "$+" #'" $ +!4!&( R, $- (9( 3(" '+ 61:; 0 8 31+ 0:
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N |
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R = |
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∑[(xi − x)( yi − y)] |
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i=1 |
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(6.3) |
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N |
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∑(xi − x)2 |
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∑( yi − y)2 |
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i=1 |
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i =1 |
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/6 x ! y — ' 6&! '#(#!'#!4 '2! *1+,#(# $ !*3 &!0 xi |
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' #$ #'#$ && : |
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x = |
∑xi , |
y = |
∑ yi . |
(6.4) |
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i 1 |
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+" 6 3 &'# (5!! () #- ' 5 &2 0 2 788!5! ( 2 +"5!! (6.3)(''3 # !3 '&(4(+( '# 0 !3 .
+() (# & 0 () # « (# 3(#!4 '2!0 3("#&!2» 6+" 6 + &!" 1'2 &!" '$ ) 6& / (6 &!" g !' +,*1 #'" *($!'!3 '#, 3 961 -
! 6 3 2 + )(&!" 3("#&!2( T ! 6+!& 0 &!#! L. !" 6( # '+ 61:;!0 $!6 7# 0 *($!'!3 '#!:
T = 2π |
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L |
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(6.5) |
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g |
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(2!3 ) (* 3, ' /+('& # !! 3 961 $ +!4!&(3! L ! T 2 6 +9&( '1; '#$ $(#, +!& 0&(" *($!'!3 '#,. $ !3 7# 1#$ 96 &! , !'-+,*1" *1+,#(#- 72' !3 (, ' 3 ;,: ('4 #( $ +!4!&- R 8 31+ (6.3).
1'#, $ -#(. !*3 &!" ! 6( 2 + )(&!0 $ 6!+!', 6+" "#!(*+!4&-. 6+!& &!#!. *1+,#(#- '$ 6 &- $ #()+!51 5. '# '#$ && , 6+" 2(96 0 6+!&- ! 6 !*3 "+'" & '2 +,2 (* ! $ #()+. 5 *(& ' &- 19 1' 6& &&- *&(4 &!" 2$(6 (#( ! 6(.
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()+!5( 5 |
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3 -#( |
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+!&( &!#! |
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17 |
24 |
31 |
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L ('3) |
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$(6 (# ! 6( |
0,4132 |
0,6954 |
0,9801 |
1,2618 |
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1,546 |
T2 (c2) |
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' +,*1" 6(&&- #()+. 5, & ). 6!3 $-4!'+!#, 5 &21 2 788!5!- 2 +"5!! R. &(4(+( $-4!'+" 3 ' 6&! *&(4 &!" 6+!&- ! 2$(6-(#( ! 6(:
L = 24 ('3), T 2 = 0,9793 ('2) .
(# 3 6'4!#( 3 # ! '133-, & ). 6!3- 6+" !3 & &!" 8 31-
+- (6.3):
∑5 (Li − L )(T 2i − T 2 )= 19,824 ('3 '2) .
i=1
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5 |
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∑(Li − |
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∑(T 2i − T 2 )2 = 0,802 ('4) . |
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,, 6'#($+"" $-4!'+ &&- '133- $ (6.3), +14!3 4!'+ && *&(4 &! !)+!9 && / 2 788!5! ( 2 +"5!!:
R = 0,999999 .
5 &2( 2 788!5! ( 2 +"5!!, '# +, )+!*2(" 2 6!&!5 , "$+" #- '" 1) 6!# +,&-3 6 2(*(# +,'#$ 3 &(+!4!" +!& 0& 0 *($!'!3 '#! 3 9-
61 $ +!4!&(3! L ! T 2 ! 72' !3 (+,&-3 6#$ 96 &! 3 # #!-
4 '2 0 8 31+- (6.5). ) +,% #+!4! +14 && 0 $ +!4!&- R #6!&!5- )1'+ $+ & / %& '#"3! !*3 &!" 6+!&- &!#! ! ! 6( 2 + )(&!0.
!$ 6 &&-0 !3 "$+" #'" # !$!(+,&-3, ( +14 &&-0 *1+,- #(# — 9!6( 3-3.
(''3 # !3 3 & 4 $!6&1: *($!'!3 '#, 3 961 6$13" 8!*!4 '2!- 3! $ +!4!&(3!.
72' !3 !''+ 61 #'" '# +2& $ &! 6$1. '#(+,&-. %( $,6$ % &&-. &( &!#". 6!&(2 $ 0 6+!&-. $-0 %( #2+ &" #'" #(2,
4# / &!#, ' '#($+" # 1/ + ϕ ' $ #!2(+,:, ! # 1'2( #'" ' &1+ $ 0 &(4(+,& 0 '2 '#,: ('3. !'. 5).
ϕ
!'. 5. . 3( '# +2& $ &!" 1 1/!. %( $
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-#( 3'" #$ #!#, &( $ ': *($!'!# +! $ 3" '# +2& $ &!" # &(4(+,& / 1/+( #2+ & &!"? 6 $ 3 & 3 '# +2& $ &!" &!3( #'" ! $(+ $ 3 &!, $ # 4 &! 2 # / %( -, 1 1/ 6 8 3! 1"',, - )-$(:# $ 2 (2# . () (# &(" 1'#(& $2( *$ +" # !*3 "#, 7# # ! $(+ $ 3 &! ' # 4& '#,: 6 3!2 ' 21&6-.
1'#, $ 72' !3 )-+ !*3 & $ 3" '# +2& $ &!" T 6+" !&-
# $(+( &(4(+,&-. 1/+ $ ϕ # 5 6 15 / (61' $. +" 2(96 / 1/+( ϕ
$ 3" '# +2& $ &!" T !*3 "+ ', 6 (* ! *1+,#(# 1' 6&"+'" 8 - 31+ (2.1). +14 &&- 4!'+ $- *&(4 &!" '$ 6 &- $ #()+!51 6.
! 6
(4(+,&-0 1/ + #2+ & &!" |
3" '# +2& $ &!" |
ϕ (/ (6) |
(32') |
15 |
133,2 |
14 |
134 |
13 |
143,7 |
12 |
135,8 |
11 |
134,2 |
10 |
135,4 |
9 |
139,3 |
8 |
125 |
7 |
110,7 |
6 |
130,7 |
5 |
100 |
( $-0 $*/+"6, ' 13 &,% &! 3 1/+( ϕ $ 3" ' 16( &!" !*3 &"-#'" $ ',3( .( #!4& . +" $-"'& &!" &(+!4!" !+! #'1#'#$!" $*(!3 -
'$"*! $ +!4!& ϕ ! T '+ 61 # 96 $' / (''4!#(#, 2 788!5! 2 +"5!!.
&(4(+( 6(&&-3 #()+. 6 $-4!'+":#'" ' 6&! *&(4 &!" 1/+( &(- 4(+,& / #2+ & &!" ! $ 3 &! '# +2& $ &!":
ϕ = 10 (/ (6) , T = 129,3 (32'),
*(# 3 — # ! '133-, & ). 6!3- 6+" !3 & &!" 8 31+- (6.3):
87
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∑(ϕi − ϕ)2 = 110 (/ (62) , |
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6'#($+"" $-4!'+ &&- '133- $ 8 31+1 (6.3), +14!3 !)+!- 9 &&-0 2 788!5! 2 +"5!!:
R = 0,687 .
+14 && *&(4 &! '1; '#$ && #+!4( #'" # &1+". + 6 $(# +,- & , 3- !. 6!3 2 $-$ 61, 4# $*(!3 '$"*, !''+ 61 3-. $ +!4!& '1- ; '#$1 #, & &(, $ *3 9& , 6(+ 2( # +!& 0& 0. +" 1'#(& $+ &!" 2 &- 2 #& / *(2 &( $*(!3 '$"*! &(4(+,& / 1/+( #2+ & &!" ! $ 3 &! '# +2& $ &!" & ). 6!3 $ '#! ) + 6 )&- 72' !3 (+,- &- ! # #!4 '2! !''+ 6 $(&!" 6(&& 0 )+ 3-.
§ 6.3. ! & # (-.. $
( #$
+ 61 # 3&!#,, 4# ! '(3! *1+,#(#- !*3 &!0, ! +14( 3- !* &!. ' 6&! '#(#!'#!4 '2! 6'#($+":# ' ) 0 '+14(0&- $ +!4!&-.
+!4!&( R, 6 +" 3(" 8 31+ 0 (6.3), 2(2 81&25!" '+14(0&-. $ - +!4!&, '(3( "$+" #'" '+14(0& 0 $ +!4!& 0. ! $# &!! ' !! !*- 3 &!0 3- )16 3 +14(#,, $ ); / $ ", 6 1/! -#&- *1+,#(-
#- (6.2) ! ' 6&! *&(4 &!" (6.4). + 6 $(# +,& , 3- +14!3 6 1/ *&(4 &! 5 &2! R.
+" +14 &!" &(6 9& 0 !&8 3(5!! $*(!3 '$"*! !''+ 61 3-. $ +!4!& X ! Y # )1 #'" '# !#, 6 $ !# +,&-0 ! $(+ 6+" & !*- $ '#& / *&(4 &!" 2 788!5! ( 2 +"5!! ρ XY .
+" ('4 #( / (&!5 6 $ !# +,& / ! $(+( & ). 6!3 *&(#,(' 6 + &! $ "#& '# 0 '+14(0& 0 $ +!4!&- R. 3(# 3(#!4 '2 0 '#(#!'#!2 1'#(& $+ & , 4# 7# (' 6 + &! $ ); 3 '+14( *($!'!#
# !'#!&& / *&(4 &!" 2 788!5! ( 2 +"5!! ρ XY , 2 # & !*- $ '#& 72' !3 (# 1. 7# 31 '# &! 6 $ !# +,& / ! -
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$(+( 6'#($+" # ' ) 0 6 '#(# 4& '+ 9&1: 3(# 3(#!4 '21: )+ - 31.
!9 !*+(/( #'" (+/ !#3, 2 # -0 6( # &(6 9&- *1+,#(#- 6(9 6+" & ) +,% / 2 +!4 '#$( !*3 &&-. ( *&(4 &!0 !''+ 61 3-. $ -
+!4!& X ! Y.
(6(6!3'" (2(2 $' /6( ! '# &!! 6 $ !# +,& / ! $(+()
6 + && 0 6 $ !# +,& 0 $ "#& '#,: α.
( $ 3 %(/ # )1 #'" 6 +!#, 4!'+ ε, 2 # "$+" #'" 2 & 3 '+ 61:; / & +!& 0& / 1 ($& &!"
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α = 2 Φ(ε) , |
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(6.6) |
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/6 Φ(x) — 81&25!" ( +('( |
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Φ(x) = |
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∫exp |
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81&25!! ( +('( ('3. !+ 9 &! 4). *(6(&& 31 *&(4 &!: 81&25!!( +('( α/2 !* #()+!5- !*$+ 2( #'" ' #$ #'#$1:;(" $ +!4!&( ( /1- 3 ( ε. ( ! #'1#'#$!! $ #()+!5 4!'+ $ / *&(4 &!" α/2 '+ 61 #
!3 &!#, +!& 0&1: ! +"5!:.) |
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$ !# +,&-0 ! $(+ 6+" 2 788!5! ( 2 +"5!! ρ XY |
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'#($!3 $ $!6 : |
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th(U − ε |
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(N − 3) |
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/6 U — $ +!4!&(, 2 # (" '$"*(&( ' |
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8!5! ( 2 +"5!! R '+ 61:;!3 ) (* 3: |
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ln |
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1&25!" th(z) — /! ) +!4 '2!0 #(&/ &', 2 # -0 3 9& $- (- *!#, 4 * 72' & &5!(+,&1: 81&25!: 16$ && / ( /13 (:
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th(z) = |
exp(2z) −1 |
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(6.10) |
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exp(2z) + 1 |
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(3 #!3, 4# 19 $-4!'+ &! / (&!5 6 $ !# +,& / ! $(+( (6.8)
# )1 # ) + # . ( !*3 &!0.
$ 3 &&(" 2 3 ,:# &(" # .&!2( ! / (33& ) ' 4 &! - *$ +":# + /2 $ 6!#, $-4!'+ &!", & ). 6!3- 6+" '# &!" / (&!5 6 $ !# +,& / ! $(+( (6.8). $ *) (&" #'" !' +,* $(#, ' )'#$ && 14& ' '#($+ &&- / (33- '+ !. # '#! $(&!".
6+ 9 &&-0 ' ' ) '# &!" 6 $ !# +,& / ! $(+( 6+" 2 - 788!5! ( 2 +"5!! 6( # &(6 9&- *1+,#(#- ! +:) 3 *&(4 &!!
$ +!4!&- ρ XY , '+! 4!'+ ( N !*3 &&-. *&(4 &!0 xi, yi (i = 1,…N) & 3 & 6 '"#2(.
'+! 4!'+ !*3 &!0 $ +!2 (& '2 +,2 ' # &) !+! !*$ '#& , 4#(*) ' *&(4 &!0 ) !. !''+ 61 3-. $ +!4!& X ! Y 64!&" #'" & - 3(+,& 31 *(2 &1 (' 6 + &!" $ "#& '# 0, # / (&!5- 6 $ !# +,-
& / ! $(+( 6+" ρ XY |
$- (9(:#'" ) + '# 0 8 31+ 0: |
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R − ε(1 − R) |
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≤ ρXY ≤ R + ε(1 − R) |
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, |
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N |
N |
(6.11) |
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/6 ( (3 # ε - 9& 31 6 +" #'" !* 1 ($& &!" (6.6).
31+ (6.8) ! (6.11) 6 '#(# 4& , 4# )- $-4!'+"#, / (&!5- 6 $ !-
# +,& / ! $(+( 6+" 2 788!5! ( 2 +"5!! $ ); 3 '+14( .6&(2 !3 # '3-'+ (''3 # #, $(9&-0 6+" (2#!2! 4('#&-0
'+14(0, 2 /6( 8!*!4 '2(" # !" !. 6!# 2 $-$ 61 # 3, 4# !''+ - 61 3- 8!*!4 '2! $ +!4!&- X ! Y 3 /1# '4!#(#,'" & *($!'!3-3!.
# *&(4!#, 4# 2 788!5! 2 +"5!! ρ XY 6 +9 & ($&"#,'" &1+:.
$ 2( '6 +(&& / # #!4 '2 / $-$ 6( *(2+:4( #'" $ +14 &!! 72' !3 (+,&-. *1+,#(# $ (6.2) ! $-4!'+ &!! 5 &2! 2 788!5!-
( 2 +"5!! R 8 31+ (6.3). ! 7# 3 +14( #'" !)+!9 &- & *&(4 &! 2 788!5! ( 2 +"5!!, 2 # 3 9 # *&(4!# +,+!4(#,'" # &1+" !*-*( '+14(0&-. / %& '# 0 *1+,#(# $ !*3 -
&!0 xi , yi (i = 1,… N).
2(*(& , 4# ! 1'+ $!! ρ XY = 0 '+14(0&(" $ +!4!&(
90