Please show code input (all steps) and output using RStudio in an Rmarkdown file (either copy code or show screenshots of R please)! Thank you!

tractor data for second question (copy into excel and make .csv file)

age	cost
4.5	619
2.5	1049
2.5	1033
4	495
4	723
4	681
5	890
5	1522
5.5	987
5	1194
0.5	163
0.5	182
6	764
6	1373
1	978
1	466
1	549

transforms data for second question (copy into excel and make .csv file)

X1	Y1	X2	Y2	X3	Y3	X4	Y4
0.29907355	0.726536348	0.109946044	1.176509321	1.403281312	-1.307394244	0.299592093	-4.428982981
1.319732734	17.48013643	0.87143679	0.039689075	0.746645153	0.700949877	1.351840152	6.891305522
2.957786477	52.65884293	0.514419769	0.304709566	3.383857487	-11.40480471	0.214564428	-3.822781767
0.095780353	0.092437367	0.285698822	0.401837917	2.414022816	-3.387714521	1.887721835	4.64118773
1.535912534	16.10884208	0.336734021	0.887898259	-0.662179483	4.89598765	2.019705633	7.648734125
1.658736042	29.42992632	0.569652015	0.160304783	2.546448404	-5.178959289	0.14869131	-5.484574162
0.562851214	9.998365387	0.184229292	0.268141249	-3.127310947	1.816970251	2.557221838	8.284437937
0.578896337	5.096413424	0.43937147	0.342255678	-0.829000462	4.920924817	0.798921884	2.276643207
0.568671694	1.670625107	0.661822181	0.163946568	-1.126416711	5.86731743	0.509759224	-0.224134692
0.410640218	0.276626596	0.420338618	0.28087964	-3.715972951	0.720645328	1.56171948	5.848098442
0.620522943	2.924461424	0.560976219	0.109568668	-1.663071198	6.03705064	3.598859922	8.370466428
0.368473514	0.454948882	0.195623653	0.365558743	-1.835488487	5.838260863	4.783297366	10.17629453
0.460126469	4.71346462	0.928305026	0.061345839	1.028341267	0.517473248	0.301029794	-4.004737439
1.066581653	1.140280868	0.673574197	0.222758397	1.49156641	-1.42366923	0.645522659	0.645644208
2.610375443	22.48108394	0.131037017	0.562513633	-2.597339289	6.492867428	1.157637722	3.878563704
0.895578416	6.115798229	0.376886585	0.208798733	3.975180807	-15.99445778	1.068247094	3.932151902
0.599889681	1.546017646	0.302303068	0.104453768	2.016035201	-3.073749517	0.640801197	1.303875449
0.402043327	0.440826442	0.805257694	0.114332071	-3.732387021	0.962193361	0.096124372	-7.264866091
0.432933267	0.690992356	0.470128402	0.302185249	-3.02211331	2.626143095	0.757007311	2.20539745
11.19911972	1176.906152	0.441445996	0.511840331	-2.001698069	4.071323824	0.30672502	-1.65270124
1.143493694	16.00316208	0.079596619	1.639795379	3.683270158	-14.67713479	1.033680023	4.263068406
0.61220634	3.626539003	0.37353533	0.303572741	1.982817272	-2.000345454	0.432697239	-1.777045472
0.643683668	20.12224034	0.387934748	0.597771097	3.411361322	-12.53682503	0.889041751	3.16324588
1.583423763	40.53291528	0.390294614	0.310296475	1.315468112	0.738706924	0.476388028	-0.254098515
0.499713549	1.664803581	0.23941948	0.347683228	-1.385681663	6.737873562	0.664748192	1.077443388
0.234991741	0.142738356	0.789585664	0.061246089	1.674352132	-0.293516599	0.6853876	0.207758487
1.776696464	292.3902799	0.015871221	0.801649169	0.445572719	2.821200079	3.774872895	10.22981602
0.359279112	1.27066701	0.398760055	0.338733897	-0.77287972	4.558430293	2.047124871	6.645910282
0.984975708	2.446946615	0.388267587	0.307738937	-1.165342091	4.233274041	0.792716846	1.483718204
0.392213635	0.9268466	0.457780159	0.280017947	0.413975095	3.024956135	0.29339751	-2.208638757
3.011076169	32.7741372	0.296645798	0.453633326	-3.089399431	2.787891543	2.850624494	9.230015823
0.621516339	1.46748131	0.803237528	0.128424653	2.45754927	-5.28846631	0.237780527	-3.308472032
0.491919577	0.475710643	0.871395009	0.063878278	-3.968868418	-0.480210307	0.306521025	-5.523388103
0.605768087	2.062187136	0.944575613	0.133180076	-2.594324477	4.769794455	0.460149043	-1.778341012
0.196107271	0.26458604	0.272898909	0.548894083	-0.080081599	4.869522972	0.37820704	-0.924332229
0.311106724	0.16474726	0.675439207	0.072578572	-2.412673464	5.535488096	0.405085323	-2.263624141
0.113037049	0.002519251	0.711411033	0.103048245	-0.109681992	6.460096897	3.622643276	9.84455936
0.261585735	0.265159665	0.201657166	0.706784144	3.71536185	-13.58576836	0.899255931	2.651974668
0.745057518	2.858702999	0.556708517	0.153254825	3.597937576	-13.48028757	0.488766234	0.528047523
0.627571581	3.567683857	0.623513345	0.183041475	-3.739873894	0.912434367	1.957605801	5.648239312
4.260967577	96.30936971	0.108069493	0.898516194	-3.816029999	-0.917423608	1.218515879	3.93036576
0.343474391	0.891857743	0.584840168	0.331946436	-1.330848414	5.463251856	0.295201612	-2.75556021
0.425128147	0.301476403	0.645851398	0.103996072	-1.968552858	4.605032317	0.570658044	1.467828845
0.755313033	5.808760249	0.188579073	0.563167799	3.514159957	-11.88429832	1.705285652	5.491282337
0.369967514	1.404451015	0.457757004	0.190687896	2.484645123	-5.86819647	7.030905233	13.04198332
0.379646654	0.926872138	0.91748753	0.036296679	-1.617829161	3.89164539	4.864399278	9.566867942
0.330443961	2.121399396	0.56594591	0.072633946	1.071762584	1.031551875	2.311247732	7.821987641
0.285936396	0.612586337	0.942231293	0.065289154	-1.253392903	3.975295948	0.987015374	3.141471393
0.592249003	2.284497172	0.744742129	0.144649201	0.387624193	4.009068422	0.178031289	-4.989672468
0.60844427	2.420034756	0.716767146	0.160297733	-1.888056055	3.273185648	0.481497821	-1.064938433
0.164304929	0.208942951	0.545366402	0.097189207	-1.86097257	4.982654016	0.80620771	3.608287295
0.558737265	4.50600057	0.976736281	0.030347299	1.522959558	-0.327491701	1.632653603	5.311207239
0.329925099	0.855430062	0.943534912	0.033333852	0.637034487	0.90195381	1.061192657	3.418105868
0.362416198	1.274702106	0.176526736	0.417314161	1.31357044	1.47781396	1.060045734	3.185881088
0.850178014	1.160029356	0.545996764	0.21163517	-0.745975532	4.189252252	6.28623993	13.03812042
1.756030421	10.64459268	0.644861061	0.19449643	-0.382437667	4.148851116	1.473515289	4.169805473
5.195627845	591.1338355	0.104921181	0.485643788	0.361974269	3.341114539	0.755367627	1.798708782
0.46146299	0.313118776	0.038207727	0.212928979	-3.083949376	2.697697081	0.651474035	1.431980909
4.982389668	160.6656596	0.770915366	0.159480383	-1.746752301	4.169195369	1.100016231	2.23138479
0.314173924	0.739947251	0.957311142	0.076973733	-1.947812481	5.459482794	0.443378528	-0.838938237
1.928202968	49.32436425	0.110683428	0.505359292	3.061556226	-9.677180802	3.928234457	9.247148325
12.79418884	577.4046481	0.402247479	0.174894367	2.717332225	-6.466084894	0.75010954	2.991130635
0.965836813	5.46597532	0.027498869	0.792555928	2.843305627	-8.254624282	0.589457637	1.062135952
0.511896113	0.224678607	0.41438876	0.304491228	3.068662729	-10.157094	0.41769118	-3.090198526
0.992424087	6.908996812	0.208988368	0.766926183	3.27479369	-10.68742702	2.54948932	8.598750144
5.912592793	89.75123423	0.918075671	0.127558593	-1.365341363	5.982004265	0.278798126	-3.168595688
0.320264604	0.403966153	0.228233433	0.329841844	-1.14602866	5.549342852	0.625790368	0.094976043
3.926809167	23.50767559	0.981930832	0.060783855	0.311195845	3.24604208	1.366860184	4.206995739
3.779398201	104.9519699	0.271757604	0.862271756	-0.956514448	3.279044907	0.897338336	1.186246325
1.400000785	19.08615155	0.531536731	0.129343804	-2.074818574	6.372426694	1.285040734	4.640148938
1.006916649	3.738220514	0.945946436	0.052380494	-1.095484566	5.250964629	0.268154119	-5.219490109
0.634150648	12.4723164	0.904914017	0.027310718	0.790376263	1.086728806	0.650460016	0.709359977
0.693139547	4.697119353	0.949038276	0.066977154	3.322412994	-11.1253373	0.181934291	-5.06537288
1.912261489	47.21178864	0.301021813	0.294151211	2.933951572	-8.062701449	0.430788786	-1.127303464
7.926969937	2439.095705	0.766108538	0.063241507	-0.942438515	3.700382881	3.152672782	9.600426299
0.8577879	1.918469012	0.189389806	0.383598766	-2.789152389	4.461085123	1.287666333	4.314705784
0.248900777	0.695346701	0.101360969	0.921427465	0.311111953	3.552015836	1.089029776	5.735380035
0.485011936	3.15457876	0.085986431	0.262056855	-3.20388001	3.911891727	0.393125598	-2.527593827
1.294677672	8.329393469	0.509233312	0.175440489	1.187745051	1.552495437	0.573028626	1.755018138
0.728287701	3.648704016	0.577651121	0.1064785	1.300526517	-0.407520547	0.361906163	-3.696317774
0.837118235	1.27384017	0.686913793	0.078724498	2.009452261	-3.537611056	1.05498363	2.190309791
0.843669814	5.695163503	0.251567298	0.596077504	2.434395188	-6.3090165	2.149281513	5.924307484
0.253522707	0.159432253	0.445504526	0.313286728	-0.844196688	4.792189412	1.348772359	2.974861716
0.840475757	7.968899748	0.541231029	0.186895944	0.915074419	2.486185078	0.539228563	1.396615104
2.340190315	12.16388898	0.568181182	0.237928537	3.924088595	-13.60482366	1.738090877	6.797639888
2.008942997	27.77268053	0.930421034	0.045396714	1.328942321	0.945958983	1.473894915	6.310808993
1.733248427	6.442456822	0.172382052	0.216796755	-2.585320901	2.327791011	2.323816651	6.60713327
0.668491247	1.747542967	0.039249057	1.583224309	-2.5113771	5.114371103	0.643632359	0.882459162
0.825642201	0.721366002	0.098939085	0.662215827	-3.385169728	3.212077653	0.307473808	-1.778319375
0.302846901	0.521428137	0.015507256	0.795275923	2.495500114	-5.044220697	0.918908188	3.637684461
0.948229404	12.04396452	0.920399774	0.06839604	0.134970346	2.861466198	1.353613516	5.074025249
1.290714577	10.00492466	0.746445894	0.156238503	-3.007260539	4.296319635	4.754510427	10.9536162
5.5066916	25.92315834	0.605408891	0.201254865	3.691384042	-12.87302373	0.93270853	1.487514141
2.722398389	19.92411327	0.377696092	0.51198724	-0.087314561	4.831567832	1.532713072	5.444883269
0.609215361	9.721248565	0.341490881	0.367362807	0.168276653	3.260801718	0.920108944	2.405190194
1.426965693	62.1993091	0.327539561	0.290904133	0.537358137	3.554610179	8.639958165	13.12746413
0.32154813	0.159643042	0.627512093	0.130973406	0.349493388	3.320995887	3.811291314	11.26599756
2.406572719	20.06830907	0.63296612	0.225950265	-0.932917243	5.145313288	0.79270475	1.137074026
2.645649925	49.8439372	0.98041901	0.03453122	2.447895685	-3.902838238	0.880377849	2.60585594
8.340449446	478.5823728	0.869424938	0.045726382	2.759383168	-6.472189561	0.978548034	3.407608735
1.513649367	6.414287937	0.641573159	0.170677389	-0.3153618	1.682091307	1.11991645	4.617425184
0.622060158	0.745814972	0.409524286	0.397589105	1.086100848	0.516544564	0.568305922	0.541827344
1.068219767	4.76833083	0.920937331	0.027096422	0.330359323	1.770022097	1.084046054	5.376717251
0.605029669	5.024322217	0.451421944	0.382159768	2.587146355	-5.60549576	0.498689607	-0.033720285
0.437797595	0.98124545	0.914272625	0.06477372	3.092556734	-9.800643341	0.334137687	-2.969490833
1.181741597	3.648763169	0.026355088	0.843923938	2.098434381	-2.598134099	2.235445546	7.124714325
0.408091189	0.502848895	0.341939308	0.623541021	0.298756344	3.803374137	1.928310286	6.952349845
1.183155933	35.17023693	0.256077501	0.971868211	2.946909372	-8.384984559	0.566640238	-2.030662195
1.426135389	6.50398212	0.777131625	0.054743612	-2.192268483	4.694898308	3.570786364	9.268365156
0.949229082	9.663969062	0.296054621	0.682265313	1.066987056	0.650912711	0.824858093	2.07880613
0.822065981	14.7211813	0.25745843	0.336751541	1.228404753	0.610963318	0.753018699	1.343073033
0.522531635	2.127533469	0.471335896	0.259804195	1.28404977	-0.912941653	0.385323625	-1.716990028
0.329635681	0.356358362	0.070287146	1.030044076	-2.899824213	4.165707146	0.975943439	0.88644041
2.337949359	26.25836727	0.226595517	0.541616151	1.85782473	-2.698397638	0.871982464	2.66130646
1.022614442	3.195945568	0.114746522	0.341068549	-3.420960149	1.320726457	1.069849935	3.340621298
2.295936032	89.96639974	0.079978723	0.61070756	-1.714492017	4.8982584	1.560752942	4.733413298
0.288146038	0.357474462	0.440887099	0.575319535	-0.390660267	6.541527778	2.475891141	4.668583219
1.184151416	33.03191198	0.982425559	0.057218393	-0.29894237	2.77286069	1.387370968	4.225840095
1.960434842	10.95896662	0.963837146	0.036537235	-2.916290069	3.105158403	2.698137248	8.081016672
0.974065844	2.483746011	0.797595503	0.06582531	-2.913176712	3.567993737	2.902001218	8.255842102
0.825808668	3.934507575	0.541736203	0.334063038	1.754830802	-2.356893742	0.053371304	-12.26110771
0.457532826	1.072307927	0.455775707	0.302920351	-2.001649456	4.587079371	0.695743833	1.507776573
7.831562067	185.1766739	0.211034197	0.339020106	-0.467306133	5.153179338	1.768147765	4.939173158
2.118061859	4.613763996	0.230638948	0.502186237	-2.960257044	3.570686851	0.326398754	-1.898896314
6.197886224	197.9314856	0.591099796	0.228786932	-2.226091135	4.061816455	0.382643949	-0.977519418
1.083351678	2.86618104	0.258238051	1.090418699	3.231667763	-9.728660007	1.314868252	5.326225771
0.531841749	4.175483959	0.757403648	0.066331812	3.581554795	-12.604277	0.643120423	1.591729827
0.220184792	0.093497201	0.551546069	0.158086775	-0.731662255	5.748169018	0.177020839	-6.009566298
0.529352969	4.322011761	0.097625328	1.227744843	-0.350173876	3.281117782	2.474045943	7.504327392
1.253953716	4.10825334	0.150506396	0.506070327	-3.692130988	0.392472112	0.431348193	0.040875164
2.755751955	50.87077969	0.145785795	1.34014188	3.379552195	-11.51783668	1.471596484	5.542681233
1.28756152	20.36139909	0.990568211	0.08628655	-2.238999356	5.677211324	1.510483978	5.409033605
0.309762838	0.285589141	0.026092317	0.403411786	-0.361213004	4.095538521	4.578029398	11.88552293
1.951726428	33.15869987	0.606734346	0.2002429	1.26682811	-0.770183308	1.217213507	3.355975335
0.192030525	0.168851166	0.102120599	0.362060751	-1.032226589	6.03707987	1.945677709	6.353315036
0.693605275	0.772997462	0.509425602	0.104285491	-2.078259297	5.382503979	3.12861712	10.00446446
0.728973187	2.028145125	0.187421346	0.590341822	1.16477851	-0.57275982	0.666056266	0.718304665
0.142523833	0.513110373	0.507221891	0.224626431	-2.10980982	6.927823773	0.190984816	-5.142808424
2.509434734	25.41709003	0.385175515	0.309783804	2.787749914	-5.905487569	1.153649086	3.567976952
0.536401895	0.635027013	0.588665327	0.321790242	-1.125987427	3.912140005	3.765626725	10.86350214
0.716027539	2.428664914	0.920744045	0.073186947	3.972741928	-13.62911621	0.245053761	-3.895962321
4.035571359	113.2814361	0.583557926	0.124031813	-1.037976129	3.538789684	2.751459821	8.127898367
1.890184439	46.43768699	0.812902087	0.092651317	-2.797223229	3.828145599	0.941641318	2.018123677
0.897240177	12.63580431	0.767533048	0.077320404	0.336364377	2.101136372	1.104597952	3.078944181
1.671569121	15.44809767	0.607563519	0.15617996	-0.582156979	4.533124808	0.705236693	-0.315323197
1.490738757	35.60751719	0.53378231	0.11356807	-2.150870677	4.483275753	2.820328252	8.593852939
5.274355266	64.77313017	0.285478897	0.400893717	2.875456722	-7.629216886	4.154352082	10.96858559
1.317707394	0.832527783	0.124188471	0.725352732	-3.896969406	-0.720178719	4.810729767	9.516859647
1.659095581	8.587431951	0.483964074	0.164842638	1.06945312	-1.753753445	0.380069658	-1.435648937
1.415597884	5.981589725	0.367356792	0.339101751	-1.027214414	5.167240639	2.136749704	7.125365119
0.685753087	0.231987095	0.708020905	0.086427714	-0.59443512	4.177155601	0.686472128	1.314372728
1.102543147	10.66693314	0.95156857	0.041722712	1.463898094	-0.324262994	0.374033687	-1.845584459
5.148702005	60.53078407	0.30711898	0.359307629	-3.229508555	1.788213173	1.476825868	6.584408766
0.416615113	0.692254911	0.820725075	0.108962143	2.037108868	-2.394312377	0.982209441	3.243253509
1.129482992	1.304545784	0.855216085	0.069368892	-0.877971645	5.207005066	2.207199694	8.360435648
3.904503618	131.7918041	0.04594012	0.958414716	0.59500372	3.147858501	6.003831661	12.4130064
0.790870464	20.72670066	0.863778416	0.12168456	-0.586311739	3.919862282	2.819943601	8.67090802
0.348755977	0.252737264	0.476140387	0.207826496	-3.731629843	0.808131264	0.498732392	-1.018165533
0.419042218	0.78451608	0.121705234	0.659070126	-0.260705367	4.814456355	1.149839842	6.389020741
0.676970874	16.08515695	0.65589569	0.180493629	-2.046113344	4.862913297	4.109270397	10.00641139
0.428549052	2.336266397	0.22755855	0.269346432	3.572362693	-11.06201933	3.236322312	8.374712114
0.770558739	20.11002707	0.460189921	0.330001929	-3.595518369	-0.467686232	0.204992562	-4.541490763
0.660723583	2.171383326	0.886233608	0.053601265	-1.423502127	6.083361036	2.576494929	8.141329782
0.832725854	2.977476912	0.793329014	0.052391545	-3.953054082	0.200549392	0.711404506	2.021175497
1.502388384	6.779602358	0.045780544	0.3601108	-3.539943138	2.627202014	0.535067329	-1.041738028
1.867560676	73.20603568	0.067791622	0.570715771	-3.453545799	1.863049165	0.332471137	-2.643196236
5.35593742	39.64682493	0.662651305	0.076302083	1.521644443	-3.519594489	0.732131263	3.015315978
0.933612645	5.926091092	0.228873497	0.27919507	-3.324529983	2.779991109	1.991038786	5.960364824
0.725539391	2.51290525	0.592312936	0.381634041	-0.356559765	4.399389118	4.200786955	9.820168876
4.353611441	900.8071067	0.330171705	0.202586474	-1.561572514	4.304908161	1.149017349	4.304757765
5.497697663	82.27464496	0.999303025	0.082154462	-0.647668779	4.324262526	0.929552133	2.028702921
1.044192686	1.205190707	0.708791808	0.156648224	0.010584893	4.034409733	0.816820481	3.122832313
0.71701586	3.243831016	0.003169789	0.636415312	1.899768334	-0.054313015	2.595552324	8.191464968
0.16166396	0.125596409	0.769733962	0.073181162	-3.573690997	1.75710506	0.339190478	-2.316417526
4.101129398	36.3370413	0.200231169	0.446733409	-3.985388273	-0.921409589	1.284049434	2.658379529
0.432755475	1.068829509	0.689499255	0.138998369	-0.229367433	6.322888269	2.777696482	7.760942889
0.325054378	0.401072759	0.74985346	0.088591192	-1.680748988	4.804290323	2.891720088	10.34355354
20.98411842	1116.786946	0.238327119	0.739665226	-3.517932162	0.924253207	1.517509054	4.799445895
1.264935722	13.2013152	0.952966778	0.049526679	-0.487832101	3.549947764	0.312745302	-2.157451974
0.967288377	3.357707268	0.584783275	0.058599862	0.314740624	2.622413343	0.439954164	-2.030171266
0.065074694	0.003379656	0.799458068	0.086597651	1.820056025	-0.189397736	0.486514653	-2.193144328
0.905026921	0.288839383	0.934602503	0.023997973	2.789070278	-6.505763885	0.236153805	-3.506961374
2.653903924	19.70592221	0.076592922	1.270139583	-0.823650345	5.875027543	1.040831939	4.649428469
1.512658828	48.97757862	0.66360163	0.093982364	1.655884925	-1.221610711	3.397183425	7.57035311
2.490098235	71.67998903	0.987434667	0.029601664	-2.740679299	4.130987129	0.086579352	-8.387400335
7.269824862	890.6538841	0.252331066	0.348977996	2.847061731	-7.184167116	2.134831865	7.122871931
3.219121557	138.4017079	0.039436219	1.190420593	1.162114423	0.878738182	0.816554473	1.620504419
0.601254475	2.478684326	0.985621971	0.01991773	0.190391762	3.747082943	0.463414282	0.903615747
2.022188172	4.530062071	0.132850762	0.762125612	0.062059335	4.826819445	2.159785284	5.844899096
0.820028426	4.129577708	0.176190732	0.362513675	-1.122338567	5.134091537	1.912450031	6.124486495
0.583873582	8.419280935	0.482794811	0.233951569	0.352040021	3.457974572	1.100998371	4.14959244
0.057512173	0.000554112	0.636085044	0.208308698	-2.221670529	3.844003744	0.398661197	-2.680690787
0.454005098	0.471796242	0.98697907	0.068829591	3.010208385	-7.232462557	0.494176876	0.58165892
1.628752908	39.94613108	0.099534687	1.572830355	-3.163401995	4.214228482	0.198446832	-5.200323693
8.741069403	648.2315812	0.693682792	0.133119817	-1.649333447	3.446183048	6.559365714	13.63361785
1.649866894	29.97073916	0.001308702	0.701511783	2.082172992	-3.632248938	0.855906309	2.19873138
1.859318836	27.30194174	0.767425936	0.293633115	-3.153634137	3.398068129	0.470239214	-1.507674211
0.380639247	1.241679139	0.319979546	0.329044689	1.555427242	-0.442633676	0.115215333	-9.145277054
1.176630339	7.024404557	0.958012845	0.08456383	-3.197837185	3.486901102	0.650859371	-0.520374294
0.125150591	0.031319126	0.195397579	0.886302464	3.579055898	-13.21100065	0.577453185	0.105303383

Warm-up and Review 1 Data Analysis and Understanding 1.1 Maintenance Costs Revisit the model and data for tractor maintenance costs from Homework 4, Question 1.2 (iv). Esti mate o 2, and use it to give a 90% prediction interval for a 2.5 year old tractor, taking uncertainty in your estimates of Bo and B into account. Then, plot a summary of the 90% predictive distribution 1 (i.e., predictive mean and 90% interval) for tractors ranging from brand new to twelve years old Comment on what you observe. 1.2 Regression Residuals and Transformations The file transforms csv on the course website contains 4 pairs of Xs and Ys. For each pair: (i) Fit the linear regression model Y Bo B1X +E, EN NO, o 2). Plot the data and fitted line. (ii) Provide a scatterplot, normal Q-Q plot, and histogram for the studentized regression residuals Ciii) Using the residual scatterplots, state how the SLR model assumptions are violated. (iv Determine the data transformation to correct the problems in (iii), fit the corresponding regres- sion model, and plot the transformed data with new fitted line. (v) Provide plots to show that your transformations have (mostly) fixed the model violations. Warm-up and Review 1 Data Analysis and Understanding 1.1 Maintenance Costs Revisit the model and data for tractor maintenance costs from Homework 4, Question 1.2 (iv). Esti mate o 2, and use it to give a 90% prediction interval for a 2.5 year old tractor, taking uncertainty in your estimates of Bo and B into account. Then, plot a summary of the 90% predictive distribution 1 (i.e., predictive mean and 90% interval) for tractors ranging from brand new to twelve years old Comment on what you observe. 1.2 Regression Residuals and Transformations The file transforms csv on the course website contains 4 pairs of Xs and Ys. For each pair: (i) Fit the linear regression model Y Bo B1X +E, EN NO, o 2). Plot the data and fitted line. (ii) Provide a scatterplot, normal Q-Q plot, and histogram for the studentized regression residuals Ciii) Using the residual scatterplots, state how the SLR model assumptions are violated. (iv Determine the data transformation to correct the problems in (iii), fit the corresponding regres- sion model, and plot the transformed data with new fitted line. (v) Provide plots to show that your transformations have (mostly) fixed the model violations