Microsoft Word - Quiz3.docxQuiz3byJamesD.Wilson(UniversityofSanFrancisco)1. You fit a regressionmodel to two different data sets at once (you’re a...

This topic is about shrinkage method, ridge and lasso method, and diagnostic.


Microsoft Word - Quiz3.docx Quiz3 byJamesD.Wilson(UniversityofSanFrancisco) 1. You fit a regressionmodel to two different data sets at once (you’re a greatmulti- tasker),andlookatthequantile-quantile(qq)plotsofthestandardizedresidualsfor eachfit.Theseareshownabove. (a) Comment(briefly)onthemodelassumptionsofthelinearregressionmodelforFit 1andFit2. (b) Whattransformation(ifany)wouldyouapplyto thedatasets foreach fit?Give justificationforyourchoices. (c) Let’snowfocusonthedataassociatedwithFit2.Onewaytoformallytestwhether ornottheresidualsarenormalistousetheKolmogorov-Smirnov(K-S)hypothesis test.Thenullhypothesisofthetestisthattheerrorsarenormallydistributed. Youtry(forhours)manytransformationsontheresponsevariableassociatedwith Fit2andnomatterhowmuchyoutry,youkeeprejectingthenullhypothesisofthe K-S test. You decide to stop trying and livewith the fact that you cannot get a satisfactoryresultfromthetest.Describespecificallytheeffectsthatthisresulthas onthepropertiesoftheleastsquaresestimatorsofyourfittedregressionmodel. Cassia Magsie Cassia Magsie Cassia Magsie Cassia Magsie Cassia Magsie 1 2. Now you fit three regression models on three different data sets and look at the residualsagainstthefittedvalues.Theseareshownabove. (a) Discusseachplotandwhattheysuggestaboutthemodelassumptionsforeachfit. (b) Describehowyouwouldgoaboutaddressingthediagnosesyoumadein(a). 3. Letβ1be the LASSO coefficient estimateswhenλ=1 and letβ100be the LASSO coefficientestimatesfromthesamedatawhenλ=100.Whatcanwesayabouthowthe L1-normofβ1compareswiththatofβ100? 4. SupposeHankcreatedanEtsywebsite to sell craftbowties.He collectsdataon 1000peoplevisitinghiswebsiteandrecords1200differentpiecesofinformationfor eachperson(age,clicks,howdidtheyenduponhissite,howmanybowtiestheylooked at,etc).LetXdenotethe1000×1200datamatrixrepresentingthisdata.Heisinterested inunderstandingtherelationshipofthe1200characteristicsherecordedwiththetime ittakeshimtosellacraftbowtie(Y).Answerthefollowingquestions: (a) Whatcanyousayabout(XTX)−1? (b) Name3methodsyoucouldusefordevelopingapredictivemodelthatpredictsthe timetosellacraftbowtieasafunctionofX. (c) SayyoufitaLASSOregressionofYonXandfindthattheLASSOestimatorforage is0.50.Whatdoesthissayabouttheeffectofageonthetimeittakestosellacraft bowtie? (d) SayyoufitaRidgeregressionofYonXandfindthattheRidgeestimatorforageis 0.25.Whatdoesthissayabouttheeffectofageonthetimeittakestosellacraft bowtie?