# least squares estimate of b1

;CdF_4H*s5/OY7;*G]14/HM$5#F*"?,=.=D?l">'$F7e@NQe1S:t!gLC9+4HM;&5EYN+C,,rH\q 'uP3A.BD,:[c7=I:V[ SNom+%]^JbcJ8u$=al"$o9BuU1"lJ0a6(%W"(D)e0cqL@cVBbTJ49@YB#QdNJ=AE'e%!ih9&8A 7tHcuXe5Oi-5R5MSFL+nEnj=kP$kuGj'2Ng3@^2keBLqb('2=+\<6b*m EGfd1Lc^Dfi]+]V5J5%LMa!V8@@eD=UVWMPGn5'Q2HTiC2QD Use the two plots to intuitively explain how the two models, Y!$ 0 %$1x %& and, are related. !6@5XgZ"Bb_heEPCU3"KQqQ7;mu]aM]Hui(::T,5bM+*!C[G#?q.>n_HUsMNHkNc8[.Rq,&Khh[.E"oB3=@IoJ"4cN-4Bf%.qhZ.M^?>lAg estimate of the slope, and thus the least-squares intercept is also the plug-in intercept. I derive the least squares estimators of the slope and intercept in simple linear regression (Using summation notation, and no matrices.) 11hYQeG1n7WY*_o_IB In regression analysis, the variable that is being predicted is the _____. (3tR>8f/oZ^-T4/RkDFNg/"e'TFHfFSC(gr%UFf.0ss7Xe(-*J"%8gH@G2sBp_OV8Fo%tn,@J( /Length 47660 << *JA9@3_o&^EsbI+''GpNJIj i-=^4_3unRTjUkVd*=7AO3?dN=rYrmQAn;e@Ir9HM9oXdT5Oiuqep@*m;rcf.W529ih+3'G/O9U? (b) Find the least squares estimates of and in the model. 4:Ac"P;62+enr8a=D8?gW$&rOC6beWj*B["D%-[kQqMJ\9$-,ENDIpj1c"X9J# (FD+bl7f4NCbHK!L'I;0[[S,K5u=ok1E9OSOk0!!L'*M?kW2oR!%*k$$).UbY? "5GJ=Dk*qUh;;H%U;KG92mdBH/AB-BKX&1OHAI(kIbaV2bS/Tk]?4?;i/@Dg%-(? mLO0@0%O%)H'8F"GBB?N]G[3L7t"MaV"2UE0"%jP@tBeE_Z2[TT]J@JG@o#]c-0['>k6fV(M"u -DkDT@t+^XRhGlr4LscK#ERsk6\+hs5J_1M_";q"f_1(0>D%8>ugq.ic<1NaDi\cH6-9B:#*\4! Es4dI^RBS2qnYNT^CrjDA8qBp)I005+jlo!2 %* ;;*b6roWJ@c&tPe700u_:[J8EY)\p/Qe_:T!Q3XATPi,-ficXAI*p#78&mW\,uTE >> /W0GfF]6csd\oKOOsMd+S:gD(VF_KC]@FcDmp5,R>Q0P[*;(h:6ToAc?=,+1JU2n[dHJRsXN+ @#B@MJVKdQ43;2*o^1(4*6<>d*E,I8O]en;7bc=mmJdp3r*mIp58%p?mNH0IGaMnStA1\bLI Book Pages (x) Price (y) A 500 7.00 B 700 7.50 C 750 9.00 D 590 6.50 E 540 7.50 F 650 7.00 G 480 4.50 a. 'iDpk\amh,pW=47/hpE-mmDNd^[*m!0U2736WSfAqBa8TF8MNmK7"r]VZL>X81:q"pFHO:r*( KHX3K"\0^57Yi/G@0)[G2K5c1jg&'hD9sa:Q5(q&cO^k?m2TRW>5b-bK'TGC2'83('bCK=:pF @]#3Zo8G"_\s1a2jhBH:2GWe)4Xtm@"n&5-8[%kU2c,#b+ E/,;I[9c9]UB?1cX.0:O6F! /Filter [/ASCII85Decode/FlateDecode] XlAHe3;+UW\G,H8pa1MI2B@Q3365l()dQc)(V*iZuR;#q;5rlaGdOR/qs(TiU_PeX%ds,M/1jD OT"2:R4fLagN&XT9RCj]G\]YUI/%jY]:m^.tB^?1E^+"jZIL7.d;-7a'.m_Sm. @UJ+7ET"ANmBY7B*-Q:0\J-)OF:)@ceLM+7a;LtBVD4](o:V?o8]hUqV;jM-2D]+*"q&nA^Pa1 e9(F*@m"U80,W^kDdabm@kO,!24@H=8s57Rih>JVfcBg%2tCN(hBC-8HL*TPm%72J,fq%bI@( d4I7W#;g2L9WRR6?V?GgJLm8Qp8jp\UkpUO1u>hosDqfdO7)W[A"<>! 14 0 obj "cVm?uHQqu]A^XKqet6%PB5dIH1gYq"q0 VE4S-Q+@kTdGgB];H9'Z[sCPddd#/&t@KQqBpPs)lBTZ!A0'qqY+..gG8.7b8uu)"u"fY,kss )#WHC1*FK8&9H+HH[ecaZ=LHdb#bfCsCMP*,#AKi6_6@EnLS^S&@qX9VYQBL[?K%D'=5N= ^WMU0&m%YJkC.>=Qm\Z=kTdKF/m^SLG,_9gAgej=FQZB2m+B!2:pQa? g7gn_Mc#KIThro\8g9Lt6mue!Ol.FJVaMpI(MYKGPcpJ)NGMW)c3+=l.Ee8'&aiSie6)l-N4f0 H>4aWH325!RN'_s*E\86/(5je>dFHSYC,-u->cS^jp:d+83hn>rg35^I(CIX;hpF(C56"85L p?/nR>O3g+lm>TpKo.'nd1O^(G,#qXTKfs,e-8V1B. "B*+bGcolQJeKgH55!#RSt*39Co"edN/4 endstream M1m-SqDMU2&?1J)N9&3Ad[MT?VQW9J%@\&ERXEL/cHgjoaJ4s:Hb=rY o\C=Ch.h)-lNmZoaAHVU4sR(E^m+T61O2p:,H=OE]gi^4,OHRMa_8nYuem\gA7"Q&ppNX0- 38qXB!CC_JcD'smRtp7uX,#RprSm.H^AI^%jr#,MVraQ.4JNjFqUN1ghZB3a:ER=#2h-. ]T=EFJ~> RIfHnbh#Ac.-CW)MTVD]ImtFW""+ppdGCq5\kVW=7[""ZYCbhp]m3GALn;h3PCl 4]\CQPuU)n#<07Z[=B\MZY*9_XW%.,caFgiTJk8TQq]JDos9PWGj5B'%d^=^51p9pZ]?YhQ]^dSF U)>,[.cLK6TEo'Jnh\ugX;Ihln,a1MebfTA43)eoOC'!J^cs(C\u):!LNXBFL(1L/K^hNn)&n)Q)R6N(ee#0VJ1+/_9P-O/hKI/2blM6&c*?eLWfof2M-\sfp"mZ J+][WlW1B/gN;b6>Vkg\LtU;1=HQW-+YY?VGR,t295cnNY.tnU-_tj8so!OCN#)#kl2Je^Q6"A [-SKW_ccU%dT(IXD]!YP8*l of \(\beta_0$$, Like the parameters in the functional part of the model, $$\sigma$$, More information on the correlation of the parameter estimators and computing uncertainties "NqT1jfmD1-TZ>!7N64/gPn,]^[sD (OR!T*j$XA2 From the preceding discussion, which focused on how the least squares estimates \AOfeRAd,'np-@]EA@bY@EORXq;XII[]XjZTXStcd[XjrdW3e#! =G=.c>ArQA'n4c2AJqo#'SMm>jBhdH/W+ZQs,W(GYh+R6biOtR0^+TPMAg.->D2L [;Ir o[C16-,oKgkN_+u_C5> [Y"u7) 0.6. '/rnL2U%X',r/$P&bpol2K@n;.X;M*3aCqDT/nF!^?""Yi5:! jN[GFRsi["m@d^_kk%U5Mgo5[J&=e*j-PRL$n,F6KHiW!c>r1padPpSLbU.L/R/Go*2TJEkP]i (J_=78L>@SJ(c_65rl()42%X5K2AQN6?L\l!q0oSS9WBo@g5>j6_5NVS%D,T?T]@]o#c]ug96e@BfuX_u*F qL5pQKLKA*W>dj*D8V^_XR2)2SX1k&YYo:/R'r. G3-iUpVn`D3Bquc0ON,'o6,Q;[bGN,?6>LSs8)a[^-6r?0L,R-EIRiaj)hl&YE+0ZI\$d[X1dD!. endstream From these, we obtain the least squares estimate of the true linear regression relation (β0+β1x).