ISYE 6414 - Midterm 1 Prep Exam Questions And
Answers
If iλ=1 i- icorrect iAnswers i✔✔ i-we ido inot itransform
non-deterministic i- icorrect iAnswers i✔✔ i-Regression ianalysis iis ione iof ithe isimplest iways iwe ihave iin
istatistics ito iinvestigate ithe irelationship ibetween itwo ior imore ivariables iin ia i___ iway
random i- icorrect iAnswers i✔✔ i-The iresponse ivariable iis ia i___ ivariable, ibecause iit ivaries iwith
ichanges iin ithe ipredicting ivariable, ior iwith iother ichanges iin ithe ienvironment
fixed i- icorrect iAnswers i✔✔ i-The ipredicting ivariable iis ia i___ ivariable. iIt iis iset ifixed, ibefore ithe
iresponse iis imeasured.
simple ilinear iregression i- icorrect iAnswers i✔✔ i-regression ianalysis iinvolving ione iindependent
ivariable iand ione idependent ivariable iin iwhich ithe irelationship ibetween ithe ivariables iis
iapproximated iby ia istraight iline
Multiple iLinear iRegression i- icorrect iAnswers i✔✔ i-A istatistical imethod iused ito imodel ithe
irelationship ibetween ione idependent i(or iresponse) ivariable iand itwo ior imore iindependent i(or
iexplanatory) ivariables iby ifitting ia ilinear iequation ito iobserved idata
polynomial iregression i- icorrect iAnswers i✔✔ i-a iregression imodel iwhich idoes inot iassume ia ilinear
irelationship; ia icurvilinear icorrelation icoefficient iis icomputed i(we ican ithink iof iX iand iX-squared ias
itwo idifferent ipredicting ivariables)
three iobjectives iin iregression i- icorrect iAnswers i✔✔ i-1) iPrediction
2) iModeling
3) iTesting ihypothesis
Prediction i- icorrect iAnswers i✔✔ i-We iwant ito isee ihow ithe iresponse ivariable ibehaves iin idifferent
isettings. iFor iexample, ifor ia idifferent ilocation, iif iwe ithink iabout ia igeographic iprediction, ior iin itime,
iif iwe ithink iabout itemporal iprediction
,Modeling i- icorrect iAnswers i✔✔ i-modeling ithe irelationship ibetween ithe iresponse ivariable iand ithe
iexplanatory ivariables, ior ipredicting ivariables
Testing ihypotheses i- icorrect iAnswers i✔✔ i-of iassociation irelationships
useful irepresentation iof ireality i- icorrect iAnswers i✔✔ i-We ido inot ibelieve ithat ithe ilinear imodel
irepresents ia itrue irepresentation iof ireality. iRather, iwe ithink ithat, iperhaps, iit iprovides ia i___
β0 i- icorrect iAnswers i✔✔ i-intercept iparameter i(the ivalue iat iwhich ithe iline iintersects ithe iy-axis)
β1 i- icorrect iAnswers i✔✔ i-slope iparameter i(slope iof ithe iline iwe iare itrying ito ifit)
epsilon i(ε) i- icorrect iAnswers i✔✔ i-is ithe ideviance iof ithe idata ifrom ithe ilinear imodel
to ifind iβ0 iand iβ1 i- icorrect iAnswers i✔✔ i-to ifind ithe iline ithat idescribes ia ilinear irelationship, isuch
ithat iwe ifit ithis imodel.
simple ilinear iregression idata istructure i- icorrect iAnswers i✔✔ i-pairs iof idata iconsisting iof ia ivalue ifor
ithe iresponse ivariable,and ia ivalue ifor ithe ipredicting ivariable. iAnd iwe ihave in isuch ipairs
modeling iframework ifor ithe isimple ilinear iregression: i- icorrect iAnswers i✔✔ i-1) iidentifying idata
istructure
2) iclearly istating ithe imodel iassumptions
linear iregression iassumptions i- icorrect iAnswers i✔✔ i-1) ilinearity
2) iconstant ivariance iassumption
3) iindependence iassumption
linearity iassumption i- icorrect iAnswers i✔✔ i-mean izero iassumption, imeans ithat ithe iexpected ivalue
iof ithe ierrors iis izero.
A iviolation iof ithis iassumption iwill ilead ito idifficulties iin iestimating iβ0, iand imeans ithat iyour imodel
idoes inot iinclude ia inecessary isystematic icomponent.
constant ivariance iassumption i- icorrect iAnswers i✔✔ i-which imeans ithat ithe ivariance i(σ^2) iof ithe
ierror iterms ior ideviances iis iconstant ifor ithe igiven ipopulation. iA iviolation iof ithis iassumption imeans
ithat ithe iestimates iare inot ias iefficient ias ithey icould ibe iin iestimating ithe itrue iparameters
Independence iAssumption i- icorrect iAnswers i✔✔ i-which imeans ithat ithe ideviances iare iindependent
irandom ivariables.
Violation iof ithis iassumption ican ilead ito imisleading iassessments iof ithe istrength iof ithe iregression.
, normality iassumption i- icorrect iAnswers i✔✔ i-errors i(ε) iare inormally idistributed. iThis iis ineeded ifor
istatistical iinference, ifor iexample, iconfidence ior iprediction iintervals, iand ihypothesis itesting. iIf ithis
iassumption iis iviolated, ihypothesis itests iand iconfidence iand iprediction iintervals ican ibe imisleading.v
third iparameter i- icorrect iAnswers i✔✔ i-the ivariance iof ithe ierror iterms i(σ^2)
One iapproach iis ito iminimize ithe isum iof isquared iresiduals ior ierrors iwith irespect ito iβ0 iand iβ1. iThis
itranslated iinto ifinding ithe iline isuch ithat ithe itotal isquared ideviances ifrom ithe iline iis iminimum. i-
icorrect iAnswers i✔✔ i-How ican iwe iget iestimates iof ithe iregression icoefficients ior iparameters iin
ilinear
regression ianalysis?
fitted ivalues i- icorrect iAnswers i✔✔ i-to ibe ithe iregression iline iwhere ithe iparameters iare ireplaced
by ithe iestimated ivalues iof ithe iparameters.
Residuals i- icorrect iAnswers i✔✔ i-are isimply ithe idifference
between iobserved iresponse iand ifitted ivalues, iand ithey iare iproxies iof ithe ierror iterms iin
the iregression imodel
MSE i- icorrect iAnswers i✔✔ i-The iestimator ifor isigma isquare iis isigma isquare ihat, iand iis ithe
sum iof ithe isquared iresiduals, idivided iby in i- i2.
σ^2 i(sample idistribution iof ithe ivariance iestimator) i- icorrect iAnswers i✔✔ i-is ichi-squared idistribution
iwith in i- i2 idegrees iof ifreedom i(We
lose itwo idegrees iof ifreedom ibecause iwe ireplaced ithe itwo iparameters iß0 iand iß1 iwith
their iestimators ito iobtain ithe iresiduals.)
epsilon ii ihat i- icorrect iAnswers i✔✔ i-proxies ifor ithe ideviances ior ithe ierror iterms
sample ivariance iestimator i(s^2) i- icorrect iAnswers i✔✔ i-the iestimator iof ithe ivariance iof ithe ierror
iterms i(is ichi-square iwith in i- i1 idegrees iof ifreedom)
positive ivalue ifor iß1 i- icorrect iAnswers i✔✔ i-a idirect irelationship
between ithe ipredicting ivariable ix iand ithe iresponse ivariable iy
negative ivalue iof iß1 i- icorrect iAnswers i✔✔ i-an iinverse irelationship ibetween ix iand iy.
ß1 iis iclose ito izero. i- icorrect iAnswers i✔✔ i-there iis inot ia isignificant iassociation ibetween ithe
ipredicting ivariable ix, iand ithe iresponse ivariable iy.
Answers
If iλ=1 i- icorrect iAnswers i✔✔ i-we ido inot itransform
non-deterministic i- icorrect iAnswers i✔✔ i-Regression ianalysis iis ione iof ithe isimplest iways iwe ihave iin
istatistics ito iinvestigate ithe irelationship ibetween itwo ior imore ivariables iin ia i___ iway
random i- icorrect iAnswers i✔✔ i-The iresponse ivariable iis ia i___ ivariable, ibecause iit ivaries iwith
ichanges iin ithe ipredicting ivariable, ior iwith iother ichanges iin ithe ienvironment
fixed i- icorrect iAnswers i✔✔ i-The ipredicting ivariable iis ia i___ ivariable. iIt iis iset ifixed, ibefore ithe
iresponse iis imeasured.
simple ilinear iregression i- icorrect iAnswers i✔✔ i-regression ianalysis iinvolving ione iindependent
ivariable iand ione idependent ivariable iin iwhich ithe irelationship ibetween ithe ivariables iis
iapproximated iby ia istraight iline
Multiple iLinear iRegression i- icorrect iAnswers i✔✔ i-A istatistical imethod iused ito imodel ithe
irelationship ibetween ione idependent i(or iresponse) ivariable iand itwo ior imore iindependent i(or
iexplanatory) ivariables iby ifitting ia ilinear iequation ito iobserved idata
polynomial iregression i- icorrect iAnswers i✔✔ i-a iregression imodel iwhich idoes inot iassume ia ilinear
irelationship; ia icurvilinear icorrelation icoefficient iis icomputed i(we ican ithink iof iX iand iX-squared ias
itwo idifferent ipredicting ivariables)
three iobjectives iin iregression i- icorrect iAnswers i✔✔ i-1) iPrediction
2) iModeling
3) iTesting ihypothesis
Prediction i- icorrect iAnswers i✔✔ i-We iwant ito isee ihow ithe iresponse ivariable ibehaves iin idifferent
isettings. iFor iexample, ifor ia idifferent ilocation, iif iwe ithink iabout ia igeographic iprediction, ior iin itime,
iif iwe ithink iabout itemporal iprediction
,Modeling i- icorrect iAnswers i✔✔ i-modeling ithe irelationship ibetween ithe iresponse ivariable iand ithe
iexplanatory ivariables, ior ipredicting ivariables
Testing ihypotheses i- icorrect iAnswers i✔✔ i-of iassociation irelationships
useful irepresentation iof ireality i- icorrect iAnswers i✔✔ i-We ido inot ibelieve ithat ithe ilinear imodel
irepresents ia itrue irepresentation iof ireality. iRather, iwe ithink ithat, iperhaps, iit iprovides ia i___
β0 i- icorrect iAnswers i✔✔ i-intercept iparameter i(the ivalue iat iwhich ithe iline iintersects ithe iy-axis)
β1 i- icorrect iAnswers i✔✔ i-slope iparameter i(slope iof ithe iline iwe iare itrying ito ifit)
epsilon i(ε) i- icorrect iAnswers i✔✔ i-is ithe ideviance iof ithe idata ifrom ithe ilinear imodel
to ifind iβ0 iand iβ1 i- icorrect iAnswers i✔✔ i-to ifind ithe iline ithat idescribes ia ilinear irelationship, isuch
ithat iwe ifit ithis imodel.
simple ilinear iregression idata istructure i- icorrect iAnswers i✔✔ i-pairs iof idata iconsisting iof ia ivalue ifor
ithe iresponse ivariable,and ia ivalue ifor ithe ipredicting ivariable. iAnd iwe ihave in isuch ipairs
modeling iframework ifor ithe isimple ilinear iregression: i- icorrect iAnswers i✔✔ i-1) iidentifying idata
istructure
2) iclearly istating ithe imodel iassumptions
linear iregression iassumptions i- icorrect iAnswers i✔✔ i-1) ilinearity
2) iconstant ivariance iassumption
3) iindependence iassumption
linearity iassumption i- icorrect iAnswers i✔✔ i-mean izero iassumption, imeans ithat ithe iexpected ivalue
iof ithe ierrors iis izero.
A iviolation iof ithis iassumption iwill ilead ito idifficulties iin iestimating iβ0, iand imeans ithat iyour imodel
idoes inot iinclude ia inecessary isystematic icomponent.
constant ivariance iassumption i- icorrect iAnswers i✔✔ i-which imeans ithat ithe ivariance i(σ^2) iof ithe
ierror iterms ior ideviances iis iconstant ifor ithe igiven ipopulation. iA iviolation iof ithis iassumption imeans
ithat ithe iestimates iare inot ias iefficient ias ithey icould ibe iin iestimating ithe itrue iparameters
Independence iAssumption i- icorrect iAnswers i✔✔ i-which imeans ithat ithe ideviances iare iindependent
irandom ivariables.
Violation iof ithis iassumption ican ilead ito imisleading iassessments iof ithe istrength iof ithe iregression.
, normality iassumption i- icorrect iAnswers i✔✔ i-errors i(ε) iare inormally idistributed. iThis iis ineeded ifor
istatistical iinference, ifor iexample, iconfidence ior iprediction iintervals, iand ihypothesis itesting. iIf ithis
iassumption iis iviolated, ihypothesis itests iand iconfidence iand iprediction iintervals ican ibe imisleading.v
third iparameter i- icorrect iAnswers i✔✔ i-the ivariance iof ithe ierror iterms i(σ^2)
One iapproach iis ito iminimize ithe isum iof isquared iresiduals ior ierrors iwith irespect ito iβ0 iand iβ1. iThis
itranslated iinto ifinding ithe iline isuch ithat ithe itotal isquared ideviances ifrom ithe iline iis iminimum. i-
icorrect iAnswers i✔✔ i-How ican iwe iget iestimates iof ithe iregression icoefficients ior iparameters iin
ilinear
regression ianalysis?
fitted ivalues i- icorrect iAnswers i✔✔ i-to ibe ithe iregression iline iwhere ithe iparameters iare ireplaced
by ithe iestimated ivalues iof ithe iparameters.
Residuals i- icorrect iAnswers i✔✔ i-are isimply ithe idifference
between iobserved iresponse iand ifitted ivalues, iand ithey iare iproxies iof ithe ierror iterms iin
the iregression imodel
MSE i- icorrect iAnswers i✔✔ i-The iestimator ifor isigma isquare iis isigma isquare ihat, iand iis ithe
sum iof ithe isquared iresiduals, idivided iby in i- i2.
σ^2 i(sample idistribution iof ithe ivariance iestimator) i- icorrect iAnswers i✔✔ i-is ichi-squared idistribution
iwith in i- i2 idegrees iof ifreedom i(We
lose itwo idegrees iof ifreedom ibecause iwe ireplaced ithe itwo iparameters iß0 iand iß1 iwith
their iestimators ito iobtain ithe iresiduals.)
epsilon ii ihat i- icorrect iAnswers i✔✔ i-proxies ifor ithe ideviances ior ithe ierror iterms
sample ivariance iestimator i(s^2) i- icorrect iAnswers i✔✔ i-the iestimator iof ithe ivariance iof ithe ierror
iterms i(is ichi-square iwith in i- i1 idegrees iof ifreedom)
positive ivalue ifor iß1 i- icorrect iAnswers i✔✔ i-a idirect irelationship
between ithe ipredicting ivariable ix iand ithe iresponse ivariable iy
negative ivalue iof iß1 i- icorrect iAnswers i✔✔ i-an iinverse irelationship ibetween ix iand iy.
ß1 iis iclose ito izero. i- icorrect iAnswers i✔✔ i-there iis inot ia isignificant iassociation ibetween ithe
ipredicting ivariable ix, iand ithe iresponse ivariable iy.
