# # Data generating code.
# set.seed(12)
# N <- 100
# d <- data.frame(A = rep(c('wildtype','mutant'), each=N))
# d$X1 <- ifelse(d$A=='wildtype',1+rbeta(N,5,5)*5,rbeta(N,5,5)*5)
# d$Y <- 3.3*d$X1+1+rnorm(N,sd=1)
# d$X2 <- ifelse(d$A=='wildtype',d$Y+rnorm(N,sd=1),10+0.5*d$Y+rnorm(N,sd=1))
# 
A	X1	Y	X2
wildtype	4.888013763657753	17.220148668336034	16.126224068146747
wildtype	2.6466870920555405	11.056046073101246	10.855183648903251
wildtype	2.6792735554652074	9.533928686311095	8.457578564205855
wildtype	1.786113252075942	8.372749806171884	8.632677955331438
wildtype	3.2570441325082005	11.278709526416423	10.489048601759881
wildtype	3.2186129343181396	10.755578915520076	8.752748499655997
wildtype	2.939191211557856	11.69861249915875	12.290847318879043
wildtype	3.40502431068255	11.144712361383611	10.735409268631322
wildtype	3.8819854567356566	14.664180457967648	13.204914331453322
wildtype	2.805849558285594	9.63222712530706	9.782357098569982
wildtype	2.351204856821141	9.17966080747029	8.413308547334681
wildtype	2.8042036930820347	9.857998890834574	10.494959423673787
wildtype	3.5106617228535018	12.19543556476089	12.267232513396047
wildtype	3.3640257394783886	12.484858324270931	13.005534298381459
wildtype	2.8720647746849846	12.140684038121249	12.845361222864796
wildtype	4.55765639814192	14.912126855973854	16.472752223830074
wildtype	3.803852198279388	13.421637380315337	14.53500594546085
wildtype	3.9524976897704587	13.626376381730271	13.057280407126726
wildtype	3.2382909834818427	12.338721547660631	11.42042491303276
wildtype	3.699531097217906	11.560637899826304	11.560674668604856
wildtype	5.220745799050299	17.551927319808005	17.444263831281326
wildtype	4.402202818850771	14.221801198962874	12.266953360297743
wildtype	3.230119416384137	11.254014284222976	10.94024234266933
wildtype	2.5860759098420245	10.893147294301265	10.528255920171974
wildtype	3.2614277828140765	11.101462398056784	10.832339388197322
wildtype	3.3223645993455335	11.049221331766402	11.569475949171107
wildtype	3.6169755833660546	13.064277424658016	12.64880724549037
wildtype	3.630070901691127	12.75379797883972	11.749252911149043
wildtype	3.823094986671773	14.286310687180086	14.45303732936234
wildtype	4.101626156597014	15.073163941870542	15.355240920870152
wildtype	3.0170826537439686	10.901105827010133	12.144628259234922
wildtype	2.546164696858722	9.904445790855268	9.70226782435448
wildtype	3.1676261482859465	10.812912708693025	9.246768889105706
wildtype	3.066996119851309	12.92395244120373	13.147355114872958
wildtype	3.74517675931986	14.357801401268208	13.097800497640355
wildtype	3.072023237623128	12.015404555703082	13.58496930701145
wildtype	4.212313893083406	14.445772229722758	14.140937896572616
wildtype	2.604452451805258	9.506298784872213	8.015185050482437
wildtype	3.593655605911999	12.898726164581404	13.131409616517427
wildtype	2.471084108161767	9.701647357690938	10.267349552855768
wildtype	4.016055141410261	14.027294783816654	13.700893033696037
wildtype	3.224723614983357	12.035244211951138	12.958681407444848
wildtype	3.9011424303517908	13.99735194864584	12.857094253656973
wildtype	2.6286959701475556	9.835983333953529	9.097804832363794
wildtype	3.669508032990173	11.8345602293691	10.779095944611264
wildtype	4.152902507595135	13.52737672303696	14.025598344670659
wildtype	3.06033552666305	11.225765320746776	10.361919357203613
wildtype	3.4619221808644856	14.165527565032722	13.380088284107927
wildtype	3.3994869584163703	11.632081544435634	12.12704283074366
wildtype	3.907716629637895	13.450277796284428	13.295003024827114
wildtype	5.230123166902823	18.172474585392937	18.79856244505354
wildtype	2.563441529212383	9.739187705147428	8.800899009692943
wildtype	4.1557552989672155	14.82100895935467	14.79012334257105
wildtype	3.981328624882515	14.132369201398063	14.35138772435869
wildtype	2.3336329432265996	10.445103917810291	10.579644252608754
wildtype	3.2769099405402144	11.752433728545034	12.598173314443567
wildtype	3.7803656805795365	10.940824553696672	10.73191550613275
wildtype	3.862814224028819	14.140289479710445	14.173690305017296
wildtype	4.386675655638534	16.143831672908128	16.956154970418698
wildtype	4.2636449104802905	14.89209317198665	17.29317955766563
wildtype	3.6758714152663563	12.734121424908544	13.380034586424653
wildtype	4.244565000196052	14.486974630149202	15.028564700676233
wildtype	4.255657600357993	15.92235404508057	16.624860124203277
wildtype	5.18229794558295	17.562231633069416	16.423954032227716
wildtype	4.366049848798202	16.772188326392683	16.778384974541304
wildtype	4.519344441879516	17.580323525020326	16.320110246436176
wildtype	3.031040052132065	10.76596694326955	9.514852282943583
wildtype	3.723341186504369	13.782615078404739	13.343748701750759
wildtype	3.1167716204337514	10.407310230071408	10.577093096120038
wildtype	3.337165022693971	11.860650227642493	11.234895506560086
wildtype	3.4078376442571425	13.383145468126527	15.013998341381008
wildtype	2.9342068115548257	8.399836664008632	6.853793321042376
wildtype	2.3709297084617678	10.476673349187847	10.290850537048762
wildtype	3.1573633140989	12.57910743577455	13.604903102565252
wildtype	3.9612391659331	13.190160501380303	13.095034970077904
wildtype	3.3412260242091594	12.97133395302465	12.958867948988594
wildtype	3.5037984308056367	12.660186670373365	12.630392737488988
wildtype	2.3683295405412093	5.8779246410749675	8.472278687165865
wildtype	3.3196833173341473	11.934679852085909	13.27102064554574
wildtype	3.479144072709433	12.871247143309246	11.356393429784736
wildtype	4.300437150260673	13.248532142408745	14.440976983437366
wildtype	3.342336116435772	11.39155254215267	12.503689866345063
wildtype	4.491845444132329	15.515423515458188	15.448793002686273
wildtype	3.016314414750545	11.68355560943058	10.878230661079517
wildtype	2.64079074826172	8.760134360224944	7.99333056474795
wildtype	3.835938022322469	14.516631014395697	14.26757071898749
wildtype	2.6219495320105284	8.171041374057683	8.258167140385286
wildtype	4.300794855526629	14.262290142242449	12.894105782890675
wildtype	3.6153160588146673	11.913928030813494	10.523844576707127
wildtype	4.421392983983997	15.37890856046899	15.684176316955535
wildtype	3.1945612745032546	13.194918632833428	13.350290016186767
wildtype	3.9036567159859046	14.607363766654217	14.821815830202178
wildtype	2.8798507798651265	10.271271382560265	10.091037694044262
wildtype	3.286749850998693	12.430782551888118	11.828173050364459
wildtype	2.6019345258864623	12.001838266001961	13.741860258167328
wildtype	5.1621398501746745	18.055759209427688	19.140645111341268
wildtype	3.5458794430349796	13.038748283606202	14.347195292181434
wildtype	3.007768576570714	11.084572461730401	10.124911828137229
wildtype	3.5955065229936913	13.790809118788044	14.271547300365663
wildtype	4.204312623254733	15.713790797192068	14.147846181686674
mutant	2.2820716686129296	8.620539754688117	15.509049579567787
mutant	2.842841667088558	11.703356170710205	16.85277915044546
mutant	1.4595008126105602	5.508678634890758	12.782353809090225
mutant	3.83927281634356	15.148176368255022	17.282355370021925
mutant	2.5651048078243797	8.995309754959814	15.564626620635714
mutant	2.0290087737977758	6.829885185802876	13.150716523599481
mutant	2.031821564474612	8.704292663784045	14.881959951686271
mutant	3.1666778985297506	10.358169201279374	14.237423961867032
mutant	1.4479870677014288	6.631985774154696	11.803816162571373
mutant	1.298924684368733	4.659375041381418	12.573530963184442
mutant	2.310603123096876	9.045675086180214	14.415204379962177
mutant	2.4201749894441225	8.590704168829463	13.990672146362497
mutant	2.7293322039318504	9.617048152319441	13.85762365614126
mutant	3.571091940344954	13.168176787130596	16.806316291499588
mutant	2.344739434465763	10.400510415397816	13.266066930934954
mutant	3.1161149554378627	10.155040095050467	14.065535124487468
mutant	2.8689204186296617	10.33636250747124	15.797545439843784
mutant	1.3462134271119883	5.025638314957318	12.698985751570355
mutant	3.7425637613839964	14.002821714737738	17.305786556058255
mutant	2.304298490939862	6.956370299108757	13.815501848594169
mutant	2.4014148354598057	8.24813513995938	14.471360063276194
mutant	3.183446946372302	10.199906819783925	13.88269501409717
mutant	2.788668143124695	9.797225082466817	14.216032259337451
mutant	1.8435965335845517	8.442965352651605	12.42382155940124
mutant	3.5199187194813946	11.954482489058933	15.906789481941312
mutant	2.2517408686567757	7.516163020493501	13.608726409935842
mutant	3.4418060449818126	12.486217947990019	15.776088508030156
mutant	2.827960921287066	10.10683504350632	15.707244153083073
mutant	3.256302159619922	12.415894357908979	15.595509546429902
mutant	1.3780565812721888	6.085384343298618	14.20471269243455
mutant	2.97149283836718	10.75065943626673	15.474592103415088
mutant	3.470485254261049	12.954703630282948	17.204181960738403
mutant	1.8756210807232323	6.549295985736069	13.988117422512993
mutant	3.7575639227247457	15.202826190686071	18.07336040435961
mutant	3.7727905491447906	14.448926907690478	16.975394122870785
mutant	1.3499719501612484	6.33263530707888	13.669237046263842
mutant	1.699648896385857	6.153977740620846	13.814379790334808
mutant	2.524529893783604	9.242554343400753	12.428169611980183
mutant	1.690450061171926	6.6181478669391645	12.83491342988835
mutant	2.7251440263520528	10.54004508771888	15.48495075719177
mutant	3.0733601337409326	10.91640125850787	16.059010182806997
mutant	2.1904125107064982	8.622017567837503	14.409867730507145
mutant	2.0400938775652806	7.855891724450357	14.580962297955615
mutant	2.855333071429534	10.583885768184057	14.770157387445176
mutant	3.3504879014662023	10.781793795339997	15.30812376507258
mutant	2.7321405315462535	8.838862202075651	14.70309166212582
mutant	0.7488003639294106	3.5976992837257655	10.613959961301575
mutant	2.7569472593994715	11.839110324198176	16.764427192441964
mutant	2.8229884694030467	9.729636530691668	14.469887815219094
mutant	1.0230457319624602	3.9308638339554944	11.793819896286365
mutant	3.6083777884453774	12.820714836483365	17.899453415419217
mutant	0.9570254939451235	4.438014788765472	12.534535765474637
mutant	2.698812192655795	10.013096708526984	14.600678479797583
mutant	1.9996749999899033	7.5929122392524455	13.94400363461534
mutant	2.0464650497665553	9.497449869392145	14.225273216757317
mutant	1.6625677651935709	6.425104549901111	13.525752897968987
mutant	3.935781154777371	11.453695618549528	16.05688703946452
mutant	1.9172643509561718	7.719974898570709	13.438134188866321
mutant	3.248915755284224	12.389224001738906	16.46879869790841
mutant	1.9540659696809495	7.270482667348825	13.280236531279462
mutant	2.168286686113402	7.759091818703793	14.950769121174764
mutant	2.040120016513758	7.212306183997631	12.99997786095255
mutant	2.195026136774392	9.122270215254689	17.228628231003956
mutant	3.1104948361352216	10.725281371891914	17.365422840909655
mutant	3.2125251552337355	12.965556837629945	14.475251571154493
mutant	1.7861728307790379	8.560857208388747	13.710124126988886
mutant	2.704875803943481	9.689624924247223	15.124019140101497
mutant	3.982398024720925	14.637502644519374	17.170294254701744
mutant	1.8140923880927797	6.1084687633462025	15.045650496115073
mutant	1.1400635577160831	4.610215393215464	11.216347964681386
mutant	1.3281888208715584	6.5203043509541	14.117951487106069
mutant	1.8967313980803273	4.976167799542788	12.282563757169243
mutant	2.172493585383337	9.821834143029024	16.001751192733348
mutant	2.041336237590698	8.896218083297484	15.20915004077655
mutant	1.6444631005173322	5.544799485508269	11.366761384417407
mutant	2.3914635605254744	9.83711782286849	14.862807548393368
mutant	3.0944467723088973	11.309326197334126	15.802788039147705
mutant	3.6010438385738763	9.945881824582768	15.595195494436135
mutant	3.553345988034222	12.705766665396157	14.026572662220437
mutant	3.822662233092414	14.004857072573085	16.47991019009118
mutant	2.2420408036140014	6.45582419847473	12.624229171476118
mutant	2.962808044314132	10.139109904151256	14.559750352117199
mutant	2.9253674531076928	10.346046145076889	15.840696921370585
mutant	2.7700096023082303	10.870749728370942	13.317286891661434
mutant	3.232910440165269	10.714129343506656	15.4028019646802
mutant	2.850341748639722	11.264163311242633	15.198619887803885
mutant	1.2260020906054512	3.5644148174209294	10.232906005975657
mutant	1.7246788310264658	5.761107261391911	13.752007177134509
mutant	2.454908325314965	8.084582510264475	14.091078786510849
mutant	3.653651867329391	12.845362875508787	16.592955248559395
mutant	1.3017564339965129	6.948662659161181	13.548992920258861
mutant	1.6528437556615352	7.179680997583797	13.877401029442808
mutant	2.717964229820958	9.737045767414509	14.434422807139715
mutant	1.2704283055035441	5.776921451754127	12.74308321377924
mutant	3.291518748740156	14.27746620141915	16.181790703249213
mutant	2.525131696911069	9.35363230365779	12.26107552143001
mutant	2.7490178894650326	10.409105156825376	15.508025383519026
mutant	2.432587528522065	9.18647500316986	13.27841125102271
mutant	2.609764757104991	10.537861291355332	15.082182566215986
mutant	1.5806311646186455	7.055641983692981	13.268361813076057