5>coiY\tr dvdoirtim sviovos Uneojr relationship (if one ocfck) . - i < 0 < J

Agression ClrrlS

to

T)1R6GTL7

Rtlated RekxAton

Regression

i

A MeVhod/prDCediut for dertrminirvj +he MUiCAl rtlationshipj ifOm\|) between Aorf V(UiablAj h/pical)>/ for prtcliciivt purposes.

3 Phftffiy. ,Ei-rHnj lf\^ to Ime iota _ t o L C k i i ^ s c c L ^ l

resting (cut ft* \arittb»cs SigmhConVly \ii)Wr Ytklkd ?) 3. Predicting

^-obsewe^l Value Y prtdicted value

\iav\cxb\ (xV wA\. mare. \akr

V 1

Ay S = Dt^ndth-V / Respon&e Variable

i / I W I ' / A X

NL"- t»o * k X

n=5 e ^ I k

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2«+

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— — n

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1

1 '

Characteristics at a rtqrtssvon \\oe-. —

2. Q\u)Oc\|G pas6 thru Xv\*>

/ errors

.—.—_— ——i—i—i—• — — • ——4—\cs>V——

t-residualerror=VTV? c t e t m i Minus* \red\c\edKsmarts sum c£ errors - GJ so n6V besV Une, so vke ^ S E ^ v J U n e

, 1 • „ l4rvf> *-

S S T O : -fetal Naria\\on"\ N s 06 Measured abcut -Vhrtr Mean.

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S S T O " 9 S R : reduction in ^ T O ft Oi-rrributed to reqhessun s s a

•Vo p\redibO

r= CXN| r= fxfcfficlttA of tomtatawv te\\s \ totte is relationship T or not and H>> Wit strength- -1 < r < I

the Closer tt) - I o r h ? t in t stvonqer tot relation.

r.xNj* ^N/aviancc^ \t\\e> d\rerMon oV Vmtar retortion of*4y i ———/

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'bVd- c r v o r " A A \ahe ea. roor fcf vcmunce tu c\ev- '>v m r

i . variance - A c r * dx 2 \ \0/ricxnce; * • *

n- i n - i

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<E>STO HAX=l (per fec t rrV)

OJ\t same s>gr\

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n-i 4 ~

4htrt\ a sfrt>ng (almikt perrtcV) t>4 a U S . O f l A I -* direct \\near relation bft*iwt

<£>TC 9B

Example

(almost a\ or N is LA*

<5S

tt^Q.Qfo* VP AS

o,o\ ^ . a — _ * l

W> -&7/0

11/11/2013 6:22:26 PM

Descriptive Statistics: X, Y T o t a l ^

Vari a b l e Counts/Mean SE Mean StDev Variance Sura " 3 A;" \X 5 2.000 0.707 1.581 2.500* 10.000 / ^ A - d ' ^ ^ x " Y 5 9.00 2.21 4.95 24.50*" 45.00

Correlations: X, Y Pearson c o r r e l a t i o n of X and Y = 0.990 \~x O - ^ ^ I P-Value = 0.001

Covariances: X, Y X Y

2.50000*' 7.75000 24.50000*" Cxs|=-T.T5

Regression Analysis: Y versus X

t

Co-NO nance of \^vf - rector \janancfi

The regression equation i s Y = 2.80 + 3.10 X

Pred i c t o r Constant X

Coef 2.8000 3.1000

SE Coef ,"-61.64-Y~0.2517 \

P 0.020 0.001

= 0.795822 l-Sq = 98.1% R-Sq(adj) = 97.4?

Analysis of Variance

Source DF SS MS Regression 1 96 100 96 100 Residual Error 3 1 900 0 633 T o t a l 4 98 000

F 151.74

P 0.001

Scatterplot of Y vs X

<7r* i ii V T r

C1 C2 C3 C4 X Y RESI1 FITS1

1 0 3 0.2 2.8 2 1 5 -0.9 5.9 3 2 10 1.0 9.0 4 3 12 -0.1 12.1 5 4 15 -0.2 15.2

rlf \ VtareSkiM = ^ of oredictors beina used

f-hcMW ^carter » f CCfcf- Correlate 4 ski. error i f e n a t rdodttdsiouriaJHe^ - ^ error.

4—- 5cAvrnens>vhrvil (Cartons dtetHbiitobns £ MflriftbWiiv art same.

-p. - V see p. <z&4 4_>o ,—•— 1 \

^ 4 Ex*. ATT sura £st\mates c f \-- tt\ahschc&\A £st\mates c

i . A>= s\d- rym h\t Y ^ can c.hoaEe a\t \ VYjd had

'i.o hiahscricd but WTCN uocnt; t\\V -Wit :x\me score on Vint SAT

r\o.p>.--D > OimosT ALV4ANS 4ht\tSi •* sim^\fo model to V = K |0OO=0j

nou^ X VY\ disappeared £o X SO ^ *S VYAS no rt\at\wn' to Y twoxiai.

Can A ___ So: W . 0 (x^y mre not linear rtlaVril

un\e^ B ,gt0 U i v are \\rtar rdaVtd).

un\e^ j

reject H a *\ no-v V\oeouc retated> c a ^ cnahe predictions

lot = ? ( ^ = random \jar \ablt so bi = random Nariable.

fre, vino* & Klip when h t t ^ t is pf ? NloMstMse I! ^ Hc'p)o=0 \ non-sen^-

1

MS£ s A = -A r x z • Standard error oF tsbtttifc

1 4 1 5 ?

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- w\tasu)rt x§i Yar\aWor> <>9 N& about -Vhe, VtqrcsbKr* Unt >^cc&\*rt_jiL(^

Example

t = a . a A , ,

MOY\\OA

VrtA vttiwcfe'. Ivail b t Condi tonal on X Mate)

. ^ u x u i X 6 our tocjjrf

a Types of TvcAcMonSy

TO H|2

. ( j l o t d - ^ Mean or^ (bra (Jwith i L — \s> ifleanyaxa apa ter^y vurio scored \$on W ?

foavrt^ VrAeml] fepnSer iW-tlrW) WhtaimlTtsV / P t e k i i m i A n \nd\Nldual 3 nt\ Ma\Ut for y>

for i t OjiMtn t wVx)dvb p r e d i o n for \rdiv UJho scord \ on SAT-? I wider [\oxopc std- trror)

l a ^ t r ^ m p i t S 2 t - * bd\tr estimate

3i MiH-Hciut * 0 lc\Cr-prec!)z ,

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J ! [ /n * for*)* B or

for to**:

Vn * CVlO* t 0 . 1 % «£xd2

for Conf. InV-

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