Statistics for Business and Economics: bab 16
Transcript of 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 $esign
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#eneral Linear !odel
!odels in hi)h the parameters .0 1
p all
hae e+ponents o' one are )alled linear models
3irst-4rder !odel ith 4ne (redi)tor %aria&le
Se)ond-4rder !odel ith 4ne (redi)tor%aria&le
Se)ond-4rder !odel ith To (redi)tor%aria&les
ith 5ntera)tion
y x x x x x x= + + + + + + 0 1 1 2 2 , 12
6 22
7 1 2y x x x x x x= + + + + + + 0 1 1 2 2 , 1
26 2
27 1 2
y x x= + + + 0 1 1 2 12y x x= + + + 0 1 1 2 12
y x= + + 0 1 1y x= + + 0 1 1
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#eneral Linear !odel
4'ten the pro&lem o' non)onstant arian)e )an
&e
)orre)ted &y trans'orming the dependentaria&le to a
di8erent s)ale
Logarithmi) Trans'ormations
!ost statisti)al pa)9ages proide the a&ility toapply
logarithmi) trans'ormations using either the&ase-10
.)ommon log or the &ase e: 2;1
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!odels in hi)h the parameters .0 1
p hae
e+ponents other than one are )alled nonlinearmodels
5n some )ases e )an per'orm a
trans'ormation o'aria&les that ill ena&le us to use regression
analysis
ith the general li
near model
*+ponential !odelThe e+ponential model inoles the regressione>uation
E y
x. =
0 1E y x. =
0 1
#eneral Linear !odel
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$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
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%aria&le-Sele)tion (ro)edures
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"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
%aria&le-Sele)tion (ro)edures
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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
%aria&le-Sele)tion (ro)edures
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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
Drive Fair Green Putt SandScore
2;26 660 6;2 1
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Sample $ata .)ontinued
Drive Fair Green Putt SandScore
2607 ;0, 62, 1;
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Sample Correlation CoeF)ients
Score Drive FairGreen Putt
Drive -17
Fair -2; -6;BGreen -776 -07 21
Putt 27< -1,B 101 ,7
Sand -2;< -02 267 0
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"est Su&sets Regression o' SC4R*
Vars R-sq R-sq(a) C-p s D FG P S
1 ,0B 2;B 26B ,B6
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!inita& 4utput
na!"sis of Variance
S#$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
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*nd o' Chapter 16