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1) ShortEssayForeachofthesequestions,youraudiencearepersonsthatarenotexpertsinstatistics.Writewithcompletesentencesandparagraphs.Citeanyreferencesthatyouuse.

a. Whenbuildingamodel,youmakefourassumptionsabouttheresiduals.Explainwhattheyareandhowyoucanverifythatyourassumptionsarecorrect.

b. Define'interactionterm'.Fromyourownexperience,identifyaninstanceinwhichyoubelieveaninteractiontermwouldbeappropriate.

2) Banking

a. UsetheBankingdatasetforthisquestion,foundundercontentontheD2L.Thisdatasetconsistsofdataacquiredfrombankingandcensusrecordsfordifferentzipcodesinthebank'scurrentmarket.Suchinformationcanbeusefulintargetingadvertisingfornewcustomersorforchoosinglocationsforbranchoffices.Thefieldsinthedataset:

i.Medianageofthepopulation(Age)

ii.Medianyearsofeducation(Education)

iii.Medianincome(Income)in$

iv.Medianhomevalue(HomeVal)in$

v.Medianhouseholdwealth(Wealth)in$

vi.Averagebankbalance(Balance)in$

b. LoadthedataintoR.

c. InR,youcancreateascatterplotbyusingtheplotcommand,i.e.plot(x,y).Createscatterplotstovisualizetheassociationsbetweenbankbalanceandtheotherfivevariables.Describetherelationships.

d. InR,youcancomputecorrelationsbetweentwovariablesbyusingthecorcommand,i.e.cor(x,y)wherexandyarethenamesofyourvariables,oryoucancomputepairwisecorrelationsbyusingcor(D),whereDisthenameofyourdataframe.Computecorrelationsfoundinthebankdata.Interpretthecorrelationvalues.Pastethemintoyoursubmission.Describewhichvariablesappeartobestronglyassociated?

e. Fitaregressionmodelofbalancevstheotherfivevariables.Presenttheestimatedregressionmodelandevaluateit.Recallthatyoucanbuildalinearregressionmodelbyusingthelmcommandanddisplaythemodelbyusingthesummarycommand.

f. Whichofthefivepredictorshaveasignificanteffectonbalance?(a=.05)Explain.

g. Agoodmodelshouldonlycontainsignificantindependentvariables,soremovethevariablewiththelargestpvalue(>0.05)andrefittheregressionmodelofbalanceversustheremainingfourpredictors.Presentthenewregressionmodel.

h. Analyzeifallfourpredictorshaveasignificantassociationwithbalance?(a=.05)Ifnotcontinuetoremoveoneinsignificantvariableatatimeuntilalloftheremainingpredictorsaresignificant.

i. Interpreteachoftheregressioncoefficientsforthefinalmodel.

j. DiscusstheadjR2forthefinalmodel.

k. Arethereanyinfluentialpointsinyourdataset?Explainwhatimpactaninfluencepointmighthave.

3) WATEROIL

Intheoilindustry,waterthatmixeswithcrudeoilduringproductionandtransportationmustberemoved.Chemistshavefoundthattheoilcanbeextractedfromthewater/oilmixelectrically.ResearchersattheUniversityofBergen(Norway)conductedaseriesofexperimentstostudythefactorsthatinfluencethevoltage(y)requiredtoseparatethewaterfromtheoil(Journalofcolloidandinterfacescience,Aug.1995).Thesevenindependentvariablesinvestigatedinthestudyarelistedinthetable.(Eachvariablewasmeasuredattwolevelsa"low"levelanda"high"level.)Sixteenwater/oilmixtureswerepreparedusingdifferentcombinationsofindependentvariables;theneachemulsionwasexposedtoahighelectricfield.Inaddition,threemixturesweretestedwhenallindependentvariablesweresetto0.Thevariablesaregiveninthetablebelow.

Experimentnumber

y:voltage(kw/cm)

x1:dispersephasevolume(%)

x2:salinity(%)

x3:temperature(0 C)

x4:timedelay(hours)

x5:surfactantconcentration(%)

x6:span:triton

x7:solidparticles(%)a. UseRtoperformaregressionanalysisontheWATEROILdataset

Considerinteractiontermsandsecondorderterms.Evaluatethettests,FTestandadjR2accordingly.

b.Pasteyourfinalmodelintoyoursubmission

c.Describeyourmodel.AssumeyouraudienceisafellowDSC423student.Yourdescriptionshouldbeginbyreportingbasicfactsaboutyourmodel;butshouldalsoincludeananalysisofthefindings.

Banking data set:

Age Education Income HomeVal Wealth Balance

35.9 14.8 91033 183104 220741 38517

37.7 13.8 86748 163843 223152 40618

36.8 13.8 72245 142732 176926 35206

35.3 13.2 70639 145024 166260 33434

35.3 13.2 64879 135951 148868 28162

34.8 13.7 75591 155334 188310 36708

39.3 14.4 80615 181265 201743 38766

36.6 13.9 76507 149880 189727 34811

35.7 16.1 107935 276139 211085 41032

40.5 15.1 82557 182088 220782 41742

37.9 14.2 58294 123500 132432 29950

43.1 15.8 88041 194369 267556 51107

37.7 12.9 64597 119305 186156 34936

36 13.1 64894 141011 160017 32387

40.4 16.1 61091 194928 113559 32150

33.8 13.6 76771 159531 197264 37996

36.4 13.5 55609 123085 105582 24672

37.7 12.8 74091 143750 217869 37603

36.2 12.9 53713 112649 117441 26785

39.1 12.7 60262 126928 161322 32576

39.4 16.1 111548 230893 331009 56569

36.1 12.8 48600 105737 106671 26144

35.3 12.7 51419 104149 111168 24558

37.5 12.8 51182 106898 88370 23584

34.4 12.8 60753 95869 143115 26773

33.7 13.8 64601 103737 134223 27877

40.4 13.2 62164 114257 144038 28507

38.9 12.7 46607 94576 114799 27096

34.3 12.7 61446 122619 161538 28018

38.7 12.8 62024 134430 149351 31283

33.4 12.6 54986 105647 126929 24671

35 12 48182 114436 102732 25280

38.1 12.7 47388 92820 118016 24890

34.9 12.5 55273 102468 126959 26114

36.1 12.9 53892 92968 129176 27570

32.7 12.6 47923 104539 88384 20826

37.1 12.5 46176 92654 101964 23858

23.5 13.6 33088 105430 44223 20834

38 13.6 53890 108446 95013 26542

33.6 12.7 57390 111836 134434 27396

41.7 13 48439 100788 124474 31054

36.6 14.1 56803 149138 101695 29198

34.9 12.4 52392 93875 133101 24650

36.7 12.8 48631 95490 105202 23610

38.4 12.5 52500 105377 139199 29706

34.8 12.5 42401 106478 94867 21572

33.6 12.7 64792 116071 185714 32677

37 14.1 59842 106949 135329 29347

34.4 12.7 65625 129688 175000 29127

37.2 12.5 54044 108654 140726 27753

35.7 12.6 39707 89552 80124 21345

37.8 12.9 45286 108431 91928 28174

35.6 12.8 37784 92712 60721 19125

35.7 12.4 52284 92143 146028 29763

34.3 12.4 42944 86192 98778 22275

39.8 13.4 46036 99508 98343 27005

36.2 12.3 50357 90750 126613 24076

35.1 12.3 45521 82720 105346 23293

35.6 16.1 30418 139739 24999 16854

40.7 12.7 52500 94792 147222 28867

33.5 12.5 41795 94456 91806 21556

37.5 12.5 66667 78906 143750 31758

37.6 12.9 38596 95364 54453 17939

39.1 12.6 44286 93103 110465 22579

33.1 12.2 37287 75561 86591 19343

36.4 12.9 38184 80099 76438 21534

37.3 12.5 47119 88958 102993 22357

38.7 13.6 44520 96112 93915 25276

36.9 12.7 52838 101705 75040 23077

32.7 12.3 34688 82870 93750 20082

36.1 12.4 31770 74525 47446 15912

39.5 12.8 32994 89223 50592 21145

36.5 12.3 33891 72739 81880 18340

32.9 12.4 37813 86667 69643 19196

29.9 12.3 46528 88889 96591 21798

32.1 12.3 30319 67083 34367 13677

36.1 13.3 36492 172768 24999 20572

35.9 12.4 51818 80357 135185 26242

32.7 12.2 35625 64737 76321 17077

37.2 12.6 36789 86563 69764 20020

38.8 12.3 42750 77717 95192 25385

37.5 13 30412 138911 24999 20463

36.4 12.5 37083 70909 95833 21670

42.4 12.6 31563 81597 71759 15961

19.5 16.1 15395 67500 24999 5956

30.5 12.8 21433 83456 24999 11380

33.2 12.3 31250 91049 52976 18959

36.7 12.5 31344 77541 36510 16100

32.4 12.6 29733 60252 27531 14620

36.5 12.4 41607 76270 98455 22340

33.9 12.1 32813 40313 79167 26405

29.6 12.1 29375 52096 24999 13693

37.5 11.1 34896 65357 81818 20586

34 12.6 20578 113239 24999 14095

28.7 12.1 32574 50244 49662 14393

36.1 12.2 30589 69375 48890 16352

30.6 12.3 26565 64038 42543 17410

22.8 12.3 16590 67850 24999 10436

30.3 12.2 9354 91708 24999 9904

22 12 14115 53923 24999 9071

30.8 11.9 17992 46885 24999 10679

35.1 11 7741 99375 24999 6207

End of Banking dataset:

Waterfoil:

Experiment Voltage Volume Salinity Temperature Delay Surfactant SpanTriton SolidPart 1 0.64 40 1 4 0.25 2 0.25 0.5 2 0.80 80 1 4 0.25 4 0.25 2.0 3 3.20 40 4 4 0.25 4 0.75 0.5 4 0.48 80 4 4 0.25 2 0.75 2.0 5 1.72 40 1 23 0.25 4 0.75 2.0 6 0.32 80 1 23 0.25 2 0.75 0.5 7 0.64 40 4 23 0.25 2 0.25 2.0 8 0.68 80 4 23 0.25 4 0.25 0.5 9 0.12 40 1 4 24.00 2 0.75 2.0 10 0.88 80 1 4 24.00 4 0.75 0.5 11 2.32 40 4 4 24.00 4 0.25 2.0 12 0.40 80 4 4 24.00 2 0.25 0.5 13 1.04 40 1 23 24.00 4 0.25 0.5 14 0.12 80 1 23 24.00 2 0.25 2.0 15 1.28 40 4 23 24.00 2 0.75 0.5 16 0.72 80 4 23 24.00 4 0.75 2.0 17 1.08 0 0 0 0.00 0 0.00 0.0 18 1.08 0 0 0 0.00 0 0.00 0.0 19 1.04 0 0 0 0.00 0 0.00 0.0