This problem is about regression on a dataset.

1. Read the dataset using R program, and calculate average, stand deviation, and median for each variables.

2. Perform a regression for y = a + b1x1 + b2x2, and what are the estimators of b1, b2? Are b1, b2 significant?

3. Draw scatter plots of (x1, y) and (x2, y). Do you believe the relation between x1 and y is linear? Do you believe the relation between xx and y is linear? Why?

4. From question 3, can you improve the model? If your answer is yes, please estimate the new model.

Dataset:

"y" "x1" "x2"

- 3.05495802941313 -0.63023548014462 -0.354332613758743

- 3.82856966105001 0.404748071916401 -0.910633503459394

0.413120190153624 0.146652669645846 0.463375949766487

- 2.01905819128483 -0.663896159268916 -0.0151537396013737

0.404234927957442 0.887678677681834 -0.528735011816025

- 1.01689809034539 0.886949917301536 -0.74793098680675

- 3.8931483228157 -0.741682046558708 -0.440451285801828

0.745409677280488 0.666897631250322 0.843615921214223

- 0.0134929125573287 -0.0639629689976573 0.171265192795545

- 0.548385381197127 0.0999674834311008 -0.298352875281125

- 0.586521256163813 0.1053481339477 0.786865031346679

- 3.16846599042499 -0.52221048111096 -0.449910544790328

- 0.739037318203555 0.521026626229286 -0.557454572524875

- 3.27295038046426 -0.638359798584133 -0.397508251480758

- 1.35458567499282 -0.189435637556016 0.774894315283746

- 0.961187326043482 0.707096905913204 -0.658264043740928

- 0.902203878860766 0.952796978875995 -0.747514544520527

- 5.23253905172411 -0.548349077813327 -0.709427033085376

- 1.41513699187439 -0.110381541773677 0.85848619742319

- 7.52409950977752 -0.850041150581092 -0.894575194455683

- 3.79888987052443 0.323797516990453 -0.867012495640665

- 0.775626186859761 -0.224900914821774 0.580353810917586

2.13870864010988 0.673778353724629 0.112745855934918

- 4.02561564780695 -0.698997118510306 -0.485109359025955

- 5.81806880871165 -0.305455502122641 -0.880386558361351

0.0155645777929879 -0.0224535372108221 0.523923264816403

- 4.06731791051743 -0.701506274286658 0.970476095564663

- 2.92967061806901 -0.285874819848686 -0.535040324553847

3.13524873931672 0.925288096535951 0.232147284317762

- 2.48531899103985 -0.735255993437022 0.65548262745142

- 2.72052247445565 -0.979170949198306 0.343338770326227

- 2.80126732473498 -0.670715515967458 -0.275475745089352

0.395788555105033 0.620384288951755 0.930966272950172

1.62438982362884 0.737722073681653 0.715733605436981

0.235325379887347 0.028563525993377 0.475035439245403

0.824739174427465 0.254392573144287 0.447164978832006

1.84082564697146 0.68885800614953 -0.00978132663294673

- 6.99245008548897 -0.430258851498365 -0.981829314026982

0.918841591759266 0.334451295435429 0.582618223968893

- 6.47324441415643 -0.699060495942831 -0.84512461302802

3.01342452586456 0.963455724529922 0.119290007743984

- 1.19572322944141 -0.405978529714048 0.394213601946831

- 2.59300422819188 -0.769831849262118 0.586146004963666

- 2.03365046515247 -0.673598256427795 0.512344500049949

2.80670300193122 0.888083616271615 0.316986136138439

1.76953826007396 0.589727647136897 0.0276683941483498

2.96731643352393 0.949375795200467 0.113402985967696

- 1.90810399108816 -0.301823178771883 0.800377332605422

- 0.0535207843638334 0.00393976178020239 -0.0825441894121468

- 0.0657079744851479 0.620794525370002 0.996467433404177

- 3.04790389598444 -0.985781923867762 0.517278829123825

- 3.740494184056 -0.97061217809096 -0.267980734352022

0.435718091700798 0.366806845646352 0.702001043595374

2.5536202162086 0.859440443571657 0.425693298690021

- 1.41494821610056 -0.449197602923959 0.0391841689124703

- 3.3863026150329 0.623719390947372 -0.915276322513819

0.139869814163034 0.571757825557142 0.920621349941939

2.62239835228637 0.977804311085492 -0.0949422894045711

0.781977710605798 0.227905819192529 0.0416408833116293

- 1.64886282783744 0.420371460262686 -0.626089186407626

- 4.16368635980661 0.54005571315065 -0.961200549732894

- 0.436631040809167 0.773968314286321 -0.615259296726435

- 0.0360303928120124 0.250243459362537 -0.289080495014787

- 3.05633316616846 -0.479399929288775 -0.423449652735144

0.615081791236676 0.71814623568207 0.909560275729746

- 0.0348825187271728 -0.125023995991796 0.189152454026043

- 1.33162089369596 -0.223710484802723 0.749983626883477

- 0.0937720834125716 -0.0769977895542979 0.447539309971035

- 1.87463279638221 -0.562649613246322 -0.0833177552558482

- 2.27432069022009 -0.868128979112953 0.272959385998547

- 2.65770551189998 -0.448597946669906 -0.393928008154035

- 2.63885966793139 -0.379237805027515 0.915856588166207

- 3.93580952114262 -0.915648947935551 0.872410191223025

- 5.08123016231978 -0.630653073545545 -0.687736257445067

- 2.75545687029132 -0.633253543637693 -0.255482958164066

1.17135655775344 0.510924832895398 0.65019747801125

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- 3.49023591291949 0.735689324792475 -0.970161429606378

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1.28336918595638 0.343997856602073 -0.00256341695785522

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- 4.4059039031973 -0.600046940147877 -0.596870377194136

1.88806250174821 0.713050001766533 0.546906627714634

1.22782754010989 0.943030857015401 0.916145162656903

- 0.972984035163856 -0.352555126417428 0.154468216001987

- 1.80387879491504 0.466382866725326 -0.666497461963445

- 5.40360163405041 -0.319863519631326 -0.836465927306563

2.9756820733303 0.953510369174182 0.428850180935115

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- 1.99975890561703 -0.240002241451293 -0.347737344447523

- 1.37676379609102 0.120775260496885 0.94618992228061

- 3.66111039458444 -0.072383641730994 -0.727743608411402

- 3.23087808968438 -0.606446346733719 -0.372930868528783

- 4.64215457406713 -0.146113194525242 -0.790378971025348

- 6.44475913316999 -0.813949625007808 -0.769421751145273

- 4.15543544575831 -0.769381746184081 0.968969303648919

- 0.0404851191973202 -0.119936691597104 0.233742186799645

- 1.50255748366638 -0.598130540922284 0.266294916626066

- 2.44829014572344 -0.144721854478121 -0.483245445415378

2.90485380861836 0.961199963465333 0.408748082816601

- 0.654408712358885 0.657844251021743 -0.599658095743507

- 1.77053525305464 -0.426052290014923 0.662140532396734

- 1.40618311364603 0.191833793651313 -0.520901645068079

1.31871989381306 0.797943892423064 0.84490981278941

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0.783538516614958 0.47262274986133 0.698970259167254

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1.10930239526997 0.745392680633813 0.861460972577333

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0.404875197639691 0.514423140324652 -0.325972456950694

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1.88506943986316 0.838552511762828 0.708577958401293

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2.97456735067459 0.927519489079714 0.146539281122386

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1.13185188688078 0.635593438986689 -0.252578278072178

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0.798205106424713 0.258939654100686 0.528681118506938

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0.661876132606688 0.460401880089194 0.624768923036754

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1.7064401488705 0.559761054813862 0.0407868344336748

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