statistics for business and economics: bab 16

7/24/2019 Statistics for Business and Economics: bab 16

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Slides Prepared by

JOHN S. LOUCKSSt. Edwards University

2002 South-Western/Thomson Learning


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Chapter 16Regression Analysis !odel "uilding

#eneral Linear !odel $etermining When to Add or $elete %aria&les Analysis o' a Larger (ro&lem %aria&le-Sele)tion (ro)edures Residual Analysis !ultiple Regression Approa)h to Analysis o' %arian)e and

*+perimental $esign


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#eneral Linear !odel

!odels in hi)h the parameters .0 1

p all

hae e+ponents o' one are )alled linear models

3irst-4rder !odel ith 4ne (redi)tor %aria&le

Se)ond-4rder !odel ith 4ne (redi)tor%aria&le

Se)ond-4rder !odel ith To (redi)tor%aria&les

ith 5ntera)tion

y x x x x x x= + + + + + + 0 1 1 2 2 , 12

6 22

7 1 2y x x x x x x= + + + + + + 0 1 1 2 2 , 1

26 2

27 1 2

y x x= + + + 0 1 1 2 12y x x= + + + 0 1 1 2 12

y x= + + 0 1 1y x= + + 0 1 1


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4'ten the pro&lem o' non)onstant arian)e )an

&e

)orre)ted &y trans'orming the dependentaria&le to a

di8erent s)ale

Logarithmi) Trans'ormations

!ost statisti)al pa)9ages proide the a&ility toapply

logarithmi) trans'ormations using either the&ase-10

.)ommon log or the &ase e: 2;1


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!odels in hi)h the parameters .0 1

p hae

e+ponents other than one are )alled nonlinearmodels

5n some )ases e )an per'orm a

trans'ormation o'aria&les that ill ena&le us to use regression

analysis

ith the general li

near model

*+ponential !odelThe e+ponential model inoles the regressione>uation

E y

x. =

0 1E y x. =

0 1



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$etermining When to Add or $elete%aria&les

F Test

To test hether the addition o'x2to a

model inolingx1.or the deletion o'x2'rom a

model inolingx1andx2 is statisti)ally

signi?)ant

1 1 2

1 2

.SS*. -SS*. / 1

.SS*. / . 1

x x xF

x x n p

=

.SS*.redu)ed1-SS*.'ull11/ num&er o' e+tra terms!S*.'ull1

F =


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%aria&le-Sele)tion (ro)edures

Stepise Regression At ea)h iteration the ?rst )onsideration is to

see hether the least signi?)ant aria&le)urrently in the model )an &e remoed&e)ause its F alue 3!5@ is less than theuser-spe)i?ed or de'ault Falue 3R*!4%*

5' no aria&le )an &e remoed thepro)edure )he)9s to see hether the mostsigni?)ant aria&le not in the model )an &eadded &e)ause its F alue 3!A is greater

than the user-spe)i?ed or de'ault F alue3*@T*R 5' no aria&le )an &e remoed and no

aria&le )an &e added the pro)edure stops


8/21 uares .SS* )an &e a)hieed



9/21 BB

"a)9ard *limination

This pro)edure &egins ith a model thatin)ludes all the independent aria&les themodeler ants )onsidered

5t then attempts to delete one aria&le at a

time &y determining hether the leastsigni?)ant aria&le )urrently in the model)an &e remoed &e)ause its F alue 3!5@is less than the user-spe)i?ed or de'ault F

alue 3R*!4%* 4n)e a aria&le has &een remoed 'rom the

model it )annot reenter at a su&se>uentstep



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"est-Su&sets Regression The three pre)eding pro)edures are one-

aria&le-at-a-time methods o8ering noguarantee that the &est model 'or a giennum&er o' aria&les ill &e 'ound

Some so'tare pa)9ages in)lude &est-su&sets regressionthat ena&les the use to?nd gien a spe)i?ed num&er o'independent aria&les the &est regressionmodel

!inita& output identi?es the to &est one-aria&le estimated regression e>uations theto &est to-aria&le e>uation and so on



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*+ample (#A Tour $ata

The (ro'essional #ol'ers Asso)iation 9eeps a

ariety

o' statisti)s regarding per'orman)e measures$ata

in)lude the aerage driing distan)e per)entage

o'dries that land in the 'airay per)entage o'

greens hit

in regulation aerage num&er o' putts

per)entage o'sand saes and aerage s)ore

The aria&le names and de?nitions are shonon the

ne+t slide


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%aria&le @ames and $e?nitions

Drive aerage length o' a drie in yards

Fair per)entage o' dries that land in the'airay

Green per)entage o' greens hit in regulation .apar-, green is hit in regulationD i' the playerEs?rst shot lands on the green

Putt aerage num&er o' putts 'or greens

that hae&een hit in regulation

Sand per)entage o' sand saes .landing in asand

trap and still s)oring par or &etter-

*+ample (#A Tour $ata


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Sample $ata

Drive Fair Green Putt SandScore

2;;6 6


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Sample $ata .)ontinued


2;26 660 6;2 1


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Sample $ata .)ontinued


2607 ;0, 62, 1;


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Sample Correlation CoeF)ients

Score Drive FairGreen Putt

Drive -17

Fair -2; -6;BGreen -776 -07 21

Putt 27< -1,B 101 ,7

Sand -2;< -02 267 0


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"est Su&sets Regression o' SC4R*

Vars R-sq R-sq(a) C-p s D FG P S

1 ,0B 2;B 26B ,B6


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1B1B

!inita& 4utput

na!"sis of Variance

S#$RC% DF SS &SF P

Regression ,;B6B B


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Residual Analysis Auto)orrelation

$ur&in-Watson Test 'or Auto)orrelation Statisti)

The statisti) ranges in alue 'rom Iero to'our

5' su))essie alues o' the residuals are

)lose together .positie auto)orrelation thestatisti) ill &e small 5' su))essie alues are 'ar apart .negatie

auto-

)orrelation the statisti) ill &e large A alue o' to indi)ates no auto)orrelation

d

e e

e

t tt

n

tt

n=

=

=

. 12

2

2

1

d

e e

e

t tt

n

t

t

n=

=

=

. 12

2

2

1


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*nd o' Chapter 16

statistics for business and economics: bab 16

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