4 LINEAR REGRESSION
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f
considers both
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wider
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relax interaction terms btwn predictors won coefficients tho
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OBLERS OF LINEAR MODELS
uple linearregression y potBelle predictions g pitpile
Itimeterfitting trainingdata i e y pay p i.e
timation Least SQUARES
APPROACH find P BI that mini wite Rss It i te
I Eat si y
www.msn.oi.se
model
accuracy
Residual standard
É
f E.gg gp
solution Be Eh
2
xi e
i e
xia
yi y
a a
Von e Get RSE
average amount that Y deviates frompopulation regression line
measures lackoffit ofmodelto thedate thehigher theworse ca eetto measured in th
R T
ofvariance of Y
FI measures a portion
g g totalvariance
explained by the motelusing X
measures
ofY
etiple linear repression Y PotBelle t BpXp t E
Leastsquares ESTIMATION RSS Y XPTY XP YinxD X napa Papa
xp
I
2N Y XP apyp
2XTX
t
XTCY Xp o
P W J'XTY
jÉÉÉIE
, relationship between responseand predictors Ho
B p Bp o
1 F to
µ 959kt large u F
findthe won related i repeat the test without me pay at time
2 p valve of each coefficient son when p la
w to choose mostimportant predictors as variable selection ideal approach Best subset selection fit one model foreach
problem needs to fit 2Pmodel
blouse
I
T accuracy of fittingtrainingdate
of tree fortest date if
new predictor useless 2 Backward selection
diction accuracy no predictioninterval I confidence interval e
f
considers both
bias off wtf
and modelbias
It
samecenter
wider
considers
only bias of Fx wit fx
of f wit th
the relationship
btwn you x
even tem e Additive effect of thangsof X on Y is independent on other predictors
p
relax interaction terms btwn predictors won coefficients tho
n assumptions of linen Wds
hey on y fwm one wa unitofX is o start
I relax polynomial regression Is Y Bo Be x B x2 NB stillline
among others
OBLERS OF LINEAR MODELS
