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isye 6414 midterm 1 study notes.

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isye 6414 midterm 1 study 6414 midterm 1 study 6414 midterm 1 study 6414 midterm 1 study 6414 midterm 1 study 6414 midterm 1 study 6414 midterm 1 study 6414 midterm 1 study notes.

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  • September 7, 2024
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  • 2024/2025
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  • ISYE 6414
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isye 6414 midterm 1 study notes




response ivariable i- i(correct ianswer) i--dependent ivariable irepresented iby iY

-the ivariable iwe iare iinterested iin imodeling

-random ivariable

predicting/explanatory ivariable i- i(correct ianswer) i--independent ivariable irepresented iby ix1, ix1, ietc.

-useful iin ipredicting ithe iresponse ivariable

-fixed ivariable

random ivariable i- i(correct ianswer) i-varies iwith ichange iin ipredictors ialong iwith iother irandom
ichanges


fixed ivariable i- i(correct ianswer) i-does inot ichange iwith ithe iresponse, ibut iis iset ibefore ithe iresponse
iis imeasured


simple ilinear iregression i- i(correct ianswer) i--relationship ibetween itwo ifactors iin ia inon-deterministic
iway


-estimate ithe irelationship ibetween iresponse iand ipredicting ivariable iwith ione istraight iline



y i= iβ0 i+ iβ1(x) i+ iε

multiple ilinear iregression i- i(correct ianswer) i--more ithan ione ipredicting ivariable

-estimate ithe irelationship iwith ia iplane



y= iβ0 i+ iβ1(x1) i+ iβ2(x2) i+ iε

polynomial iregression i- i(correct ianswer) i--can iinclude imore icomplex irelationships, ilike iquadratics...

-nonlinear irelationship, ibut ican istill ibe itranslated iinto ia ilinear iregression, ithinking iof ix iand ix-
squared ias itwo idifferent ipredicting ivariables

, y i= iβ0 i+ iβ1(x) i+ iβ2(x-squared) i+ iε

objectives iof iregression i- i(correct ianswer) i--predicting iresponse ivariable ibehavior iin idifferent
isettings


-modeling irelationship ibetween iresponse ivariable iand ipredicting ivariables

-testing ihypotheses iof iassociation irelationships

Why iuse ilinear imodels? i- i(correct ianswer) i-they iare ieasy ito iunderstand, imathematically isimple, iand
iwork iwell ifor ia iwide irange iof icircumstances


"All imodels iare iwrong, i_________________" i- i(correct ianswer) i-but isome iare iuseful

Are ilinear imodels ia itrue irepresentation iof ireality? i- i(correct ianswer) i-no

objective iof isimple ilinear iregression i- i(correct ianswer) i-fit ia inon-deterministic ilinear imodel ibetween
ithe ipredicting ivariable iX iand ithe iresponse ivariable iY


parameters ito iestimate i(never itruly iknown) iin isimple ilinear iregression i- i(correct ianswer) i-β0, iβ1, iε

simple ilinear iregression iequation i- i(correct ianswer) i-y i= iβ0 i+ iβ1x i+ iε

β0 i- i(correct ianswer) i-intercept

ε i- i(correct ianswer) i-deviance iof ithe idata ifrom ithe ilinear imodel

variance iof ithe ierror iterms

β1 i- i(correct ianswer) i-slope

data istructure iof isimple ilinear iregresion i- i(correct ianswer) i-pairs iof idata i- ione iresponse ivariable
ivalue, ione ipredicting ivariable ivalue


assumptions iof isimple ilinear iregression i- i(correct ianswer) i--linearity/mean izero iassumption

-constant ivariance iassumption

-independence iassumption

-normal idistribution iof ierror

Linearity/Mean izero iassumption i- i(correct ianswer) i-Means ithat ithe iexpected ivalue i(deviances) iof
ierrors iis izero


constant ivariance iassumption i- i(correct ianswer) i-the ivariance i(σ-squared) iof ithe ierror iterms ior
ideviances iis iconstant

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