Nonlinear Correlation Coefficients

7/30/2019 Nonlinear Correlation Coefficients

1/24

Gcrkvklb Lmldklcir Jmrrcditkml Jmchhkjkclts hrmf Pirtkid Fmfclts

Ay

Hrcg Xkmdc

MXXM Hkliljkid Zystcfs

[email protected]

Ilg

Givkg LiwrmjnkXkddilmvi Slkvcrskty

Xkddilmvi Zjemmd mh Ausklcss

500 Diljistcr IvclucXkddilmvi, PI 9;053 SZI

890-39;-7:1:

[email protected]
mailto:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]


2/24

Gcrkvklb Lmldklcir Jmrrcditkml Jmchhkjkclts hrmf Pirtkid Fmfclts

Iastrijt

Rc kltrmgujc i lmldklcir jmrrcditkml jmchhkjkclt fctrkj gcrkvcg hrmf pirtkid fmfclts teit

jil ac suastktutcg hmr tec Pcirsml jmrrcditkml jmchhkjkclt kl dklcir klstiljcs is wcdd. Wec

hdcxkakdkty mhhcrcg ay pirtkid fmfclts cliadcs mrgcrcg pirtktkmls mh tec giti wecrcay

dklcir scbfclts irc ibbrcbitcg hmr il mvcridd jmrrcditkml jmchhkjkclt. Mur jmchhkjkclt

wmrns wktemut tec lccg tm pcrhmrf i dklcir trilshmrfitkml ml tec ulgcrdyklb giti, ilg

jil idsm prmvkgc i bclcrid fcisurc mh lmldklcirkty actwccl twm virkiadcs. Rc idsm

cxtclg tec ilidysks tm i fudtkpdc lmldklcir rcbrcsskml wktemut tec igvcrsc chhcjts mh

fudtkjmddklcirkty.

Ncywmrgs? Pirtkid fmfclts, Lmldklcir jmrrcditkml, Lmldklcir fudtkvirkitc ilidysks


3/24

9

9. KLWQMGSJWKMLJecl ct id. (1090) cxpdmrc tec prmadcf mh cstkfitklb i lmldklcir jmrrcditkml (Zcc

Hkburc 9). Wecy lmtc teit i bclcrkj usc stitkstkj suje is tec Pcirsml jmrrcditkml

jmchhkjkclt gmcs lmt cxkst hmr lmldklcir jmrrcditkmls. Rc kltrmgujc i bclcrkj lmldklcir

jmrrcditkml jmchhkjkclt fctrkj gcrkvcg hrmf pirtkid fmfclts teit jil ac suastktutcg hmr tec

Pcirsml jmrrcditkml jmchhkjkclt kl dklcir klstiljcs is wcdd. Wec hdcxkakdkty mhhcrcg ay

pirtkid fmfclts cliadcs mrgcrcg pirtktkmls mh tec giti wecrcay dklcir scbfclts irc

ibbrcbitcg hmr il mvcridd jmrrcditkml jmchhkjkclt.

Pirtkid fmfclts eivc tercc fikl igviltibcs? (9) lm gkstrkautkmlid issufptkml ks

rcqukrcg, (1) pirtkid fmfclts irc kltcbritcg kltm cjmlmfkjs termube cxpcjtcg utkdkty

tecmry (Emdteiuscl, 9;59 ilg Butemhh ct id., 9;;2), ilg irc kltcbritcg kltm stitkstkjs is

Xkmdc ilg Liwrmjnk (1091) hklg teit pirtkid fmfclts jil ac uscg tm gcrkvc tec JGH ilg

PGH mh ily gkstrkautkml.

Wec pipcr ks mrbilkzcg is hmddmws? Wec lcxt scjtkml wkdd jmvcr tec gcvcdmpfclt mh tec

fcisurc hmddmwcg ay i scjtkml wkte cfpkrkjid rcsudts. Lcxt, wc cxtclg tec ilidysks tm i

fudtkgkfclskmlid lmldklcir ilidysks wkte il ippdkjitkml tm lmldklcir rcbrcsskml ilidysks.

I hklid gksjusskml ilg suffiry jmfpdctcs tec pipcr.

1. GCXCDMPFCLW MH LMLDKLCIQ JMQQCDIWKML FCIZSQCWec Pcirsml jmrrcditkml jmchhkjkclt ks rcprcscltcg ay


4/24

1

ilg ks stilgirgkzcg kl tec rilbc ^-9,9V. Wec jmvirkiljc ilg stilgirg gcvkitkml jillmt

ksmditc ilg gkhhcrcltkitc tec klhmrfitkml prcsclt kl cije mh tec hmur pmsskadc rcditkmlsekps

actwccl twm virkiadcs wecrc tec tirbct ks smfc rchcrcljc pmklt?

acdmw tirbct, acdmw tirbctacdmw tirbct, iamvc tirbctiamvc tirbct, acdmw tirbctiamvc tirbct, iamvc tirbct

Rc prmpmsc i fctemg mh pirtktkmlklb tec gkstrkautkml wkte pirtkid fmfclts tm jipturc tec

klhmrfitkml hrmf cije dklcir rcditkmlsekp cfacggcg wktekl i ak- mr fudtkvirkitc

rcditkmlsekp (dklcir mr lmldklcir). Aiscg ml tec iamvc hmur rcditkmlsekps actwccl twm

virkiadcs, i jm- mr gkvcrbclt pirtkid fmfclt ks jmlstrujtcg tm quiltkhy kt.k

1.9 Jm-Pirtkid Fmfclts

( |) { }

(|) { }

wecrcrcprcsclts tec mascrvitkml U it tkfc t, rcprcsclts tec mascrvitkml [ it tkfc t,lks tec gcbrcc mh tec DPF, qks tec gcbrcc mh tec SPF, ks tec tirbct hmr jmfputklbacdmw tirbct mascrvitkmls hmr U, ilg ks tec tirbct hmr jmfputklb iamvc tirbctmascrvitkmls hmr U. Hmr skfpdkjkty wc issufc teit .


5/24

:

1.1 Gkvcrbclt Pirtkid Fmfclts

(|) { }

(|) ( { })

1.: Gchklktkml mh Xirkiadc Qcditkmlsekps?

acdmw tirbct, acdmw tirbct (|)acdmw tirbct, iamvc tirbct ||iamvc tirbct, acdmw tirbct ||iamvc tirbct, iamvc tirbct (|)

Wm ivmkg tec adult jmvirkiljc ilg stilgirg gcvkitkml gcpclgcljc mh tec Pcirsml

jmchhkjkclt, wc jil usc tec hmddmwklb lmlpirifctrkj hmrfudi kl cquitkml 3 tm gctcrfklc

tec jmrrcditkml (dklcir mr lmldklcir) actwccl twm virkiadcs.

( |)(|)( |)(|)( |)(|)( |)(|)


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7

Wec ixkmfitkj rcditkmlsekp actwccl jmrrcditkml ilg jm- mr gkvcrbclt rcturls hmddmws.

Kh tecrc ks i -9 jmrrcditkml, tecl tec rcturls actwccl tec virkiadcs wkdd idwiys ac

gkvcrbclt,

(|)(|)(|)(|)

Kh tecrc ks i pcrhcjt jmrrcditkml actwccl twm virkiadcs, tecl tecrc wkdd ac lm gkvcrbclt

rcturls,

(|)(|)(|)(|)

Kh tecrc ks zcrm jmrrcditkml actwccl twm virkiadcs, tecl tec jm- ilg gkvcrbclt rcturls wkdd

ac mh cquid hrcqucljy mr fiblktugc (gcbrcc zcrm ilg gcbrcc mlc rcspcjtkvcdy),

( |) ( |) ( |)(|)[kcdgklb i 0 rcsudt,

^(|)(|)(|)(|)V^(|)(|)(|)(|)V


7/24

3

Gcbrcc mlc jil ac suastktutcg hmr pirifctcrs lilg q, tm bclcritc jmrrcditkmls

wecrcay tec fiblktugc mh tec tirbct gcvkitkmls irc jmfpircg> teus bclcritklb i

gcpclgcljc jmchhkjkclt.

1.7 Xksuidkzitkml mh tec Pirtktkmls Ssklb Fcils is Wirbcts?

Hkburc 9. 9stmrgcr pirtktkmlklb mh tec gkstrkautkml aiscg ml virkiadc rcditkmlsekps

wkte jm- ilg gkvcrbclt pirtkid fmfclts ml il mascrvcg lmldklcir jmrrcditkml kl i

fkjrmirriy stugy hrmf Jecl ct id. (1090).

| |

| || |

| |

[

U


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8

Hkburc 1. 1lg

mrgcr pirtktkmlklb mh tec fkjrmirriy stugy aiscg ml fcils mh pirtkid

fmfclt suascts is tirbcts.

|| hurtecrpirtktkmlcg wkte lcw fcil tirbcts, ilg .

U

[


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2

1.3 Gchklktkml mh Xirkiadc Zuascts?

||

|

|

|| ||

1.8 Gchklktkml mh Zuasct Fcils?

1.2 Gchkltkml mh Zuasct Pirtkid Fmfclts?

({ } { } )

({ } { })


10/24

5

({ } { })

({ } { } )

Hmr i :

rg

mrgcr ilidysks hmr cxifpdc, mlc lccgs tm tecl jmfputc tec 91 rcfiklklb

suasct pirtkid fmfclts (kl iggktkml tm tec hmur kgcltkhkcg kl cquitkmls ;-91 iamvc) usklb

tec ipprmprkitc suasct fcil tirbcts hmr cije quigrilt. Wec tmtid ifmult mh suasct fcils

wkdd ac dcss teil mr cquid tm wecrc L ks tec lufacr mh mrgcrs spcjkhkcg. kkWec cvcltuid lmrfidkzcg jmrrcditkml fctrkj ks ijjmfpdksecg ay iggklb idd JSPFs

ilg JDPFs (pmsktkvc jmrrcditkmls) ilg suatrijtklb GSPFs ilg GDPFs(lcbitkvc

jmrrcditkmls) kl tec lufcritmr, wekdc suffklb idd 98 jm- ilg gkvcrbclt pirtkid fmfclts

rcprcscltklb tec cltkrc gkstrkautkml kl tec gclmfklitmr pcr cquitkml 9: acdmw.


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;

Lufcritmr?

( Gclmfklitmr?

( (9:)

1.5 Lmldklcir Issmjkitkml?

Rc jil idsm gchklc tec ifmult mh lmldklcirkty prcsclt actwccl twm virkiadcs.

(||)(||)

(|)(|)

Cquitkml 97 gcsjrkacs tec ifmult mh lmldklcirkty prcsclt wecl tec lcbitkvc

jmrrcditkmls irc cquid kl hrcqucljy mr fiblktugc (gcpclgklb ml gcbrcc 0 mr 9

rcspcjtkvcdy) tm tec pmsktkvc jmrrcditkmls.

Recl cquids mlc, tecrc ks fixkfuf lmldklcirktyactwccl tec twm virkiadcs.Is ipprmijecs 0 mr , kt ks ipprmijeklb fixkfuf dklcirkty.


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90

-5

-8

-7

-10

1

7

8

5

-7 -: -1 -9 0 9 1 : 7[

U

-5

-8

-7

-1

0

1

7

8

5

-7 -: -1 -9 0 9 1 : 7

[

U

:. CFPKQKJID CXKGCLJC?Wekrg mrgcr gcbrcc mlc pirtktkmls irc semwl ilg jidjuditcg. Wec 9

stmrgcr pirtktkml ks

tec tekjn rcg dklc (pcr Hkburc 9), tec 1lg

mrgcr pirtktkml ks tec tekl rcg dklc (pcr Hkburc 1)

ilg tec :rg

mrgcr pirtktkml ks tec gmttcg adijn dklc.

Dklcir Cquidktkcs?kkk, kv

Pcirsml 9.0

9.0 0

Hkburc :. Dklcir pmsktkvc rcditkmlsekp

actwccl twm virkiadcs (U, [).

Pcirsml -9.0

-9.0

Hkburc 7. Dklcir klvcrsc rcditkmlsekp



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99

0

1

7

8

5

90

-7 -: -1 -9 0 9 1 : 7

[

U

0

90000

10000

:0000

70000

30000

80000

20000

50000

;0000

900000

0 30 900 930 100 130 :00 :30

[

U

Lmldklcir Gkhhcrcljcs?

hmr pmsktkvc UPcirsml 0.;85

0.;;; 0.0009

Hkburc 3. Lmldklcir pmsktkvc rcditkmlsekp


(pmsktkvc sncw)

Pcirsml -0.008

0.9:3 0.735

Hkburc 8. Lmldklcir rcditkmlsekp actwccl

twm virkiadcs (U, [).


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91

0

9C+17

1C+17

:C+17

7C+17

3C+17

8C+17

2C+17

0 30 900 930 100 130 :00 :30

[

U

110

170

180

150

:00

:10

:70

:80

330 800 830 200 230 500

[

U

Is tec cxpmlcltkid huljtkml kljrciscs kl fiblktugc, wc ijtuiddy hklg kt tm rctikl kts

dklcir rcditkmlsekp

Pcirsml 0.881

0.;;8 0.0009

Hkburc 2. Lmldklcir pmsktkvc rcditkmlsekp


Ilg i jmfpdctcdy lmldklcir jdustcrcg gitisct, wecrc jmchhkjkclt wckbetklb guc tm

pirtktkml mjjupiljy ks cxcfpdkhkcg.

Pcirsml -0.815

-0.00;2 9.01

Hkburc 5. Lmldklcir rcditkmlsekp actwccl

twm virkiadcs (U, [).


15/24

9:

7. FSDWKGKFCLZKMLID LMLDKLCIQ ILID[ZKZ?

Wm hklg tec 9stmrgcr ibbrcbitc jmrrcditkml hmr fmrc teil twm gkfclskmls, tec fctemg

ks skfkdir tm weit wis oust prcscltcg. Klstcig mh jm- ilg gkvcrbclt pirtkid fmfclts, wc

irc bmklb tm suastktutc jm- ilg gkvcrbclt pirtkid fmfclt fitrkjcskltm cquitkml 3. I l x

lfitrkx hmr cije mh tec kltcrijtkmls (JDPF, GDPF, GSPF ilg JSPF) pcr Xkmdc ilg

Liwrmjnk (1091), jil ac jmlstrujtcg ilg trcitcg ilidmbmusdy tm tec gkrcjt pirtkid fmfclt

jmfputitkml.

[kcdgklb,

(98)

Recrcay tec hklid rcsudt wkdd ac il cquid skzcg l xlfitrkx,

Wm gcrkvc tec mvcridd jmrrcditkml, wc lccg tm stcrkdkzc tec fikl gkibmlid mh 9s (wekje

irc scdh-jmrrcditkmls) wkte tec hmddmwklb hmrfudi,


16/24

97

Ibikl, kh tec virkiadcs irc idd acdmw mr iamvc teckr rcspcjtkvc tirbcts it tkfc t, tec JDPF

ilg JSPF fitrkjcs rcspcjtkvcdy wkdd jipturc teit klhmrfitkml. Kh tec virkiadcs irc k.k.g.,

tec dkncdkemmg teit mlc virkiadc wmudg gkvcrbc it tkfc t kljrciscs is lkljrciscs, rcgujklb

.Hurtecr mrgcr pirtktkml ilidysks jil ac trilsditcg tm tec fudtkgkfclskmlid ay jrcitklb

fitrkjcs hmr cije mh tec kgcltkhkcg suascts hmr idd mh tec virkiadcs.

7.9 Lmldklcir Qcbrcsskml Ilidysks?

Wec tirbct fcils hrmf wekje tec hmur pirtkid fmfclt fitrkjcs irc jidjuditcg idsm

scrvc is tec aisks hmr i lmldklcir rcbrcsskml. Ay pdmttklb idd mh tec fcil kltcrscjtkmls, tec

dklcir scbfclts wkdd hkt tec ulgcrdyklb, lmlpirifctrkjiddy. Wec kljrciscg mrgcr mh

pmrtkmlklb wkdd bclcritc fmrc kltcrscjtklb pmklts (fixkfuf mh ) hmr i fmrcbriludir ilidysks. Acdmw ks il cxifpdc wkte :

rgmrgcr pirtktkmlklb, bclcritklb i hkt tm tec

dklcir giti.


17/24

93

-5

-8

-7

-1

0

1

7

8

5

-7 -: -1 -9 0 9 1 : 7

[

U

1lg mrgcr JSPF

Jmmrgklitcs

(9) ,(y9)

:rg mrgcr JSPF

Jmmrgklitcs

(

9') ,(y9')

Hkburc ;. Lmlpirifctrkj rcbrcsskml pmklts hmr i dklcir rcditkmlsekp actwccl (U, [).

Rc jil idsm pcrhmrf teks ml lmldklcir rcditkmlsekps. Acdmw ks il cxifpdc wkte :rg

mrgcr pirtktkmlklb, bclcritklb i hkt tm il cxpmlcltkid rcditkmlsekp actwccl tec virkiadcs.


18/24

98

0

9

1

:

7

38

2

5

;

90

-7 -: -1 -9 0 9 1 : 7

[

U

Hkburc 90. Lmlpirifctrkj rcbrcsskml pmklts hmr i lmldklcir rcditkmlsekp actwccl

(U, [).

Bclcritklb i fudtkpdc virkiadc lmldklcir rcbrcsskml ilidysks rcqukrcs jrcitklb i

syltectkj virkiadc. Weks virkiadc, U* ks tec wckbetcg ivcribc mh idd mh tec cxpdilitmry

virkiadcs. Wec wckbetklb ks tec lmldklcir jmrrcditkml gcrkvcg hrmf tec l x l fitrkx wecrc

tec cxpdilitmry virkiadcs irc ml tec sifc rmw is tec gcpclgclt virkiadc wekje wkdd eivc

i 9.0 scdh-jmrrcditkml. Weus, il cxpdilitmry virkiadc wktemut gcpclgcljc (zcrm

jmrrcditkml) tm tec gcpclgclt virkiadc wkdd ac cxjdugcg hrmf jmlskgcritkml.

() ( )

Ilg tec lmldklcir fudtkpdc rcbrcsskml jil ac pcrhmrfcg kl nklg tm tec twm virkiadc

cxifpdc iamvc wkte fcils mh [, U* is kltcrscjtkml pmklts. Weks ks skfkdir tm i


19/24

92

lmlpirifctrkj dmjid fcils rcbrcsskml mldy tec lufacr mh fcils eis tm ac i hijtmr mh 7

guc tm tec hmur pirtkid fmfclt fitrkjcs pcr cije ilidysks.

Hkburc 99 acdmw ks tec lmldklcir jmrrcditkml fitrkx ilg tec suascquclt wckbetklbs hmr

tec fudtkpdc virkiadc lmldklcir rcbrcsskml usklb ZP[ is tec gcpclgclt virkiadc wkte WDW,

BDG, HUC, ilg BZB is cxpdilitmry virkiadcs.v Wec giti klvmdvcg 900 gikdy

mascrvitkmls hrmf 3/5/91 termube ;/12/91 hmr idd virkiadcs. Is semwl kl Xkmdc ilg

Liwrmjnk (1091) pirtkid fmfclts isyfptmtkjiddy jmlvcrbc tm tec irci mh tec huljtkml,

ilg stiakdkzc wkte ipprmxkfitcdy 900 mascrvitkmls.

Lmldklcir Jmrrcditkml Fitrkx

ZP[ WDW BDG HUC BZB

ZP[ 9.00 0.01 -0.98 -0.03 0.93

WDW 0.01 9.00 0.02 -0.33 -0.28

BDG -0.98 0.02 9.00 0.50 0.80

HUC -0.03 -0.33 0.50 9.00 0.27

BZB 0.93 -0.28 0.80 0.27 9.00

Hkburc 99. Lmldklcir jmrrcditkml fitrkx hmr 3 virkiadcs (ZP[, WDW, BDG,

HUC, BZB). Ekbedkbetcg rmw ksmditcs tec jmchhkjkclts hmr cquitkml 95.

Kl teks cxifpdc pcr cquitkml 95 mur ibbrcbitcg cxpdilitmry virkiadc ks,

Rkte tec fudtkgkfclskmlid ibbrcbitc jmrrcditkml is fcisurcg pcr cquitkml 92,


20/24

95

Ibikl, tecrc irc lm fudtkjmddklcirkty kssucs wkte tec cxpdilitmry virkiadcs, kt skfpdy

gmcs lmt fittcr kh tecy irc jmrrcditcg mr lmt. Acdmw kl hkburc 9: ks tec bripe mh teks

ilidysks wkte mur :rg

mrgcr hkt vcrsus tec 8te

mrgcr pmdylmfkid bclcritcg hrmf Cxjcd.

Wec suf mh squircs mh rcskguids ks rcgujcg ay 22% wecl kljrcisklb tec spcjkhkjitkml

hrmf i 1lg

mrgcr tm i :rg

mrgcr lmldklcir jmrrcditkml ilidysks (.072;3 tm .099 rcspcjtkvcdy).

Hkburc 91. Mur :rg

mrgcr hkt hmr i sklc wivc huljtkml mh U ilg Cxjcds 8te

mrgcr pmdylmfkid hkt wkte cquitkml.

y 6 0.0003x8- 0.0933x3+ 0.93:5x7- 0.3;02x:+ 0.391:x1+ 0.2512x

+ 0.0933

Q 6 0.;;22

-9.3

-9

-0.3

0

0.3

9

9.3

0 1 7 8 5 90 91

[

U

Zklc Rivc Huljtkml

Zcrkcs9

U

[

Qcbrcsskml


21/24

9;

Hkburc 9:. Mur :rgmrgcr hkt hmr il ulgctcrfklcg huljtkml mh U* ilg Cxjcds

8te

mrgcr pmdylmfkid hkt wkte cquitkml usklb tec ulgcrdyklb giti hrmf Hkburc

99.


22/24

10

3. GKZJSZZKML ILG ZSFFIQ[?

Wecrc ks lm irbufclt is tm wey tec pirtktkml jillmt ac hurtecr spcjkhkcg L tkfcs,

udtkfitcdy ykcdgklb i lufacr mh scbfclts. Wec pirtkid fmfclts irc gkrcjtjmfputitkmls, oust is mtecr stitkstkjs suje is fcils ilg virkiljcs. Wec mavkmus aclchkt ks

tec iakdkty tm pirsc weit wis rchcrrcg tm is lmksc kltm vidkg klhmrfitkml. Guc tm tec hijt

teit klgkvkguid mascrvitkmls irc wckbetcg ay , tec lufacr mh mascrvitkmls kl cijescbfclt wkdd wckbe tec scbfclt ijjmrgklbdy> teus ihhkrfklb mutdkcr mascrvitkml stitus hmr

suje klstiljcs wecrc i scbfclt eis fklkfid mjjupiljy.

Wec purpmsc mh teks pipcr wis tm put hmrte i lmlpirifctrkj, lmldklcir jmrrcditkml

fctrkj wecrc Jecl ct id. (1090) lmtc, tecrc ks lm jmffmldy usc stitkstkj quiltkhyklb

lmldklcir jmrrcditkml teit jil hklg i skfkdirdy bclcrkj usc is Pcirsmls jmrrcditkml

jmchhkjkclt hmr quiltkhyklb dklcir jmrrcditkml. Mur dklcir suf mh tec wckbetcg fkjrm gmcs

klgccg jipturc tec ibbrcbitc jmrrcditkml. Aut, uldknc Pcirsmls sklbdc jmrrcditkml

jmchhkjkclt, wc idsm bclcritc tec klhmrfitkml lcjcssiry tm rcjmlstrujt tec rcditkmlsekp

hrmf tec klgkvkguid pirtkid fmfclt fitrkjcs. Is hmr i gkrcjt pmdkjy stitcfclt rcsudtklb

hrmf tec lmldklcir rcbrcsskml ilidysks> kt wmudg eivc tm issufc tec hmrf mh i jmlgktkmlid

cquitkml wecrcay cije dklcir scbfclt ks gchklcg hmr i spcjkhkj rilbc mh tec cxpdilitmry

virkiadc(s).


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24/24

11

Clglmtcs?

kLcwtml prmvcg tec kltcbrid mh i pmklt kl i jmltklumus gkstrkautkml tm ac cquid tm zcrm.

kkKh lm giti cxksts kl i suasct, lm fcil ks jidjuditcg.

kkkWec emrkzmltid dklc is kl tec cquitkml

(pmklt prmaiakdkty) ykcdgs i 0 jmrrcditkml

hmr amte Pcirsmls jmrrcditkml ilg mur fctrkj.kv

Kt semudg ac lmtcg teit hmr lmrfidkzcg giti suje is dmb rcturls mr bcmfctrkj rcturls, tec

lmrfidkzitkml jmlstilt (0 mr 9 rcspcjtkvc tm tec rcturl hmrfit fcltkmlcg) semudg ac uscgritecr teil is tec tirbct tm gctcrfklc gcpclgcljc.vIdd virkiadcs kl tec rcbrcsskml irc cxjeilbc trigcg hulgs (CWHs) teit trigc kl SZ

firncts? ZP[ ks tec Z&P 300 CWH, WDW ks tec Airjdiys 10+ ycir Wrcisury Amlg CWH,BDG ks tec Bmdg Wrust CWH, HUC ks tec Curm Jurrcljy CWH, ilg BZB ks tec Z&P BZJK

Jmffmgkty Klgcx CWH.

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Nonlinear Correlation Coefficients