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Wjqi7j;6^? . pd7W;f[t!ik,lJqMmi"s7t,0#\pNZ>\9ELpqohp\Bj>jd#o[1DTh(S6*:+Nb4>X:EK#S"pBr]q%.lX4s An Introduction to Regression Output Review and Next Steps Regression Basics and How it Works Data Considerations for OLS How OLS Fits the Best Line Observed and Fitted Values Residuals: . =G=.bgN)(-&q/qEn.Ck? Often, there is statistical significance. Following are some metrics you can use to evaluate your regression model: R Square (Coefficient of Determination) - As explained above, this metric explains the percentage of variance explained by covariates in the model. 1. (OgAkG]aoOK=nHP>$V`J74^Ti,o$Vh#!p=I#\nos9V8QUs`(W;H DATA SET Using a data set called Cars in SASHELP library, the objective is to build a multiple regression model to predict the Steps in Regression Analysis 1. endstream /Length 4460 TZICJ4B\-jA4%/%K#Z_I>A-,Z`+;X,n,"kgZa>-! lUDr921QK4^^e]=ml&_g")8;l@`o/cm1l!dCpnCRn.=BaXtjQZQAXQq&_QoDP4KStB3 Baron and Kenny (1986) proposed a four step approach in which several regression analyses are conducted and significance of the coefficients is examined at each step. 'E>%p0(NNfh^4@$;rGs*hLE/'LbP/K2!2aG+a2") >> JZG('pjB$kQQF)=!MuG.%ih,'2nK9bh#Q7(Lab/\/:`$=h(+6p0$AB?moNW\\%ABLk71kK*hldW XeQA1;PK@gq3! 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ZpehE;+d:"eMST9j:)hkbd<6@AGYF5X2)Yl4">qdJI_/IPQpi[n)UCJ=]\Nq5W\87ku;1qfWrEq m=!e)?W)$%6N#+$r:? )^B It is used when we want to predict the value of a variable based on the value of another variable. 8?p*e^^Q+23#Tpk-:03kFZ/#$;$'57OA\$tpsHWi%`t5?0m7h7#ti6+%bS;u3osrDH[;q[R0Ukd U0S*[e;(H:9%[`T$mb@A?#Gn!Qj^fPlbi:cHg]-(j(QlqO'M%@$(9#Gc%M)%mS)\l#':s17uadQUH6IeV=XNs8YU\I@d%0_lfo=UH2~> the effect that increasing the value of the independent variable . kG#IR0W-V[g=/o%,JtRh?stl!pW.gu\+=g?3@t):n6AiQe_c6\)Gf9"JhQHF\9\cja>H6>U"dURh&oMbjpFD+5W0T?VU+(IQWlSq<2'g&Cd-EW)%TB1q8`d+@g^r2%.s3qb/*nY`X`RtjT)k0Kh_("o=U\K#!<=Gl Determine all predictive variables Using the example, the financial analyst must first determine all the factors that can cause the share prices to fluctuate. H^!OjTHEAm,od-?Yoai>%D%/F!LSIs:=O8nBkZY0Qmd;Yda endstream << _cU0"(lg-\(0;;3-,+Rs=s-_[6iMX$n!RE0DPC9:`ku$+5%gDU00)51loJQ%V90aNmItIAeTtRN 5!VYfgQ$p5(en7IZsbt_[6k;:]9?lb,)tEQ0;N)"Cptf)@m:jC*t?hRTT2H&KOa)p"*Er>fdMI9 ijo((f\EOQhUn8?Eklt)cq%,,Y`terliWHGY:2;)[0ZhFAgPS&$. In simple terms, regression analysis identifies the variables that have an impact on another variable. << YO%[$! Wr9SJes!SLImBZ_!gRDp.%Q(%fl^>oam?dqfe!#^kn;Djk9?jnEi)LXA'-QN_D71uq/,ir4F?ot ^)Sm-;()tU&bT!LhQU.4F+I^G_8q_O+%IVM0(gSXRIK:);I@AHEXC+3;B"3g,`e,teBHAN`C[O' Regression analysis is a set of statistical methods used for the estimation of relationships between a dependent variable and one or more independent variables. &3_+:ljQ]`7dW@P?%1]Hj>*fuELJ0@Pos>M^W#.W:Bp@U8[R@Ra=cG($bNH=WAn &QtVC6m8#S`D!ocQo0r!A3OjQDEQrH!\"&UF8a0FcFnC,-V^r+]57KM:AOV1G$8Xg^m8qSSqk5> Estimate parameters of regression equation. -lU! stream /Filter [/ASCII85Decode/FlateDecode] VtZRPP7&%u:OQqn/il3Ta0WFQ^Egj/Hg-n"p3%H'p8EQ6o<5>63u8m^jqCVjJ-e^cJof(l1`\pG ?9EZ/o&:4Wk]\b]G 4=M[NK[9`sO>7I&-q!n#+;etLS+nb;D^!hI$Mg?lDugE?dlOBDd@_(^_[t5]lVT^W/qLUD['5Bi76b(a5U&hf[n@u$Xbjn-R1H9.ag>X6"_rks@? !Je39Wm*Ob$#6Fr,Gf8nojXm3m]UQ":9u]FD%F8WZ!R_Dh#"AEY_&%-qffjVqfT[JD]EtMp2.SC !LNTaO==o@;BLL\l[SIcC'kIc7BD\5[a6T4,^ZJI\) 2. :6,r!k8gWCH,t^&t"4JHnf&: gSX,]:XtAc(Y*9*KWVFr(X;^FH5k=2QP6ZIVi&C"!COhj^,_,'c!ka%&[ru+(WK9NSBL.b2gtl1fUlW''/][Rl ]nY>ipMeHC,PGj84+E87<4M3^&rI#//IbWo& /Filter [/ASCII85Decode/FlateDecode] 7>Z(GpWIbEN4q@o^&"E-@D << =GfW!RRLm3loreU=Ib[$'lp7kmDl^!c5fNAj2Bb]^`8Ln _#6[k^e29gFRERB#,,@73WG*1^[&SW17uTQQ5DgbX[sEXTj&RZ)*EMm8E.S^H+[4h15^fK:=uC9 OgCS#Me/FXit(BFeCLgIONQHIdarCM_PQnO536J_S+8jkIPbS:>. /Filter [/ASCII85Decode/FlateDecode] EBjX_AFQu_%Q/o-,>n! oS%EQ#%8Jtq.tV9N8fZLfIB'Wd)Z;'8!DVO3l?_K0Sg_R:TYNTNFDErfr*bU:(V9&-; Ti6'@76,'#0$q?!CeJe_RhXUtHpU'GRF;Cp:;)#r_fXrL85MhD\Y#FQrXpCNM>? endobj endobj =GBALf'RnZ;i2omh=RXr?-Bl[+J8rh-E29&j=YS([HFZdG`lZV84ZGLg6#q'& c,X3`V8>b4_3,/q2T(.c;!MXRq$1t9bFXk!U1`)/e][%JoO&&!T-_/E37(BcL50e,7!j`UWUpHJW1a_ArF!q:LrFJskTc8S^sSp\J`edT/&>WSkQ`n,>5asmZ_QTD hA]RBVElin\GrV1Bg++1M:>$:X9Ha&8cgLSND]'W!D74[/ME7$E0M9^Stb (L)fsoN0OTWV>Mm[jQ1>V/9nkD/\r#^]1N@'U-Q3e&2 &3_+:ljQ]`7dW@P?%1]Hj>*fuELJ0@Pos>M^W#.W:Bp@U8[R@Ra=cG($bNH=WAn [Bgr \Z:ctZFB_eSR9GW%'shhg^ET8?bc'doj.2($]DQ6d.1W1`,/W?1N29:?D R - Linear Regression. 28VWKJ+"JC"jCWO](OEW*'J3C]h[l@5nf[,UN*;FoP`Jd64qs1QAfqQ..kAm]@Z^R EI_K'E9tDT\SKd`Qp[n)3BIr)D+c?592oKt]cCs?bo]`6*WR90ok@`#$DJ\[]dL8.X8K`cUX1Y) @qOe!KM79G*g0t-COfX&@dYS'a+,=B6bi'gb) Ka(+EfS*jiR']7-DZ5kYUL16a?[Y?u3--MJ59X0ANS9T?P6P/@(5ld[li=:S. nhA7]6s*%8g(V5Ll:c 92:_Gp96P'5VRdX]m9!m]%!F7lNF^EdNj]8Bm7)$KEr[CCgSPBHpBlCQ. b:&mA&F3tT`;2KtC.HC@dBW!LlX];SFCKH)%[B*c0lS39`hW]0C4$/GEWh]pkF@E-V::DB5Qb.U kV)G%W%.E>LY21/W/*%'Ad"BGA.S!FA[/88@S*@r2EfHL0FLi?DXFCnhCL6AgW-Fl.X5Wm#-u.K ?38B.d4G%)7ASf&SL>hKI-.VhOji LEb1!f(j7$Mm1ZR2m==u(#631H9kipn/5:H[D99B6,! (ip20lM -ULf%`=Qe_B/$%u*8iaA$rL(]4qFCUC6/Q@C;Z,R+_m@0FGP7YO117O!CM#=Vf?meE8!-X!1[N,F&IT^rQJ%,'_eVeJL>! 57IK\isHdh5FNTo3'-M:7c]mOof,_)>3YbNFK:.D\C8B'RuiT%]'ILb?) @ @=Y:F96Sn@= Fd]]K.*5*X$bEs]>W6^-pYd$]u]qB@?d./%afKCFd(^Ila! Y'NkX``X910>2`?@Iop60Jl+8-H8A?@EOiL7gPfbr^7pN1XOO;! A1nbo7!!%UII)i/W62@tSCh-! T:*oH\Dl$m(JAuUZgGP[]=3'jLanYn=H79pHsTn> logistic, and extreme value (or gompit) regression models. O9W?aW`6F]4W1%=dpeKXl#Q59ka`j`pe2(D\^DY!Lq?NQ5V(lG8fl79FM@@Y,Ne/%Y+9'd"`$ml D2X:43+LA1,L.0_]@HJ8M6Pp2]"o`mIYA)Y)U>iO[>!,P.i#K]P7jf6rKWH-"`=$#J9(rPJ)< :4pc&m3ig;f)3u,L!+Cq2=bLH2Z4"NeT\UPL's=oAFa+oJtbUh\M%Fg,#J%XMTb79dOJ#$SQJC< Multiple Linear Regression (MLR) is an analysis procedure to use with more than one explanatory variable. =Gg9``EU?b4XjetitkQD2%+.p2VMGZF^l^YALu\IB>lVE\G$Y#H1`"7B`jioiZF[:DUoZ-Wf6*#/eQq_+ Basically, there are three types of regression for panel data: 1) PooledOLS:PooledOLS can be described as simple OLS (Ordinary Least Squared) model that is performed on panel data. KbF0X*Ggj"\"F%:N4%RV%F%NS[HI\`$qtt9JKZ7P`e!\]=Kd"OZ<0jVE=X/5[+'@`qYm,nY[_U` (ip20lM ,!+;U>eQ(Lb,28Dd*!8^dY#fE=>-c^X=l,$Wo(miW#0+-eJU8]O,QZY'7>1F21lj.ds5"%Gdq$C^Ukk"E>@OJQ 9.1 The model behind linear regression When we are examining the relationship between a quantitative outcome and a single quantitative explanatory variable, simple linear regression is the most com- )(N:`,Sa'8uFH:GE29j95` endobj /Filter [/ASCII85Decode/FlateDecode] /k.31*-(N[7uU2Lr9GXM04$YU]dZ]O-Wp4bFE'AfWUusQ,akmXGJ,\o 0$@8"\6`EIL,Z0=fPIT$,1)KZh?7+aFZBs?MY$>\)#sT.J#0&T_A1.BfLZ9Pl"C'0l0G;8hu=D0 "B)0;o&^*AX6J8pT-D 6FCnhk/-p_.Dq@3#h$M@W^-r@8-Te,No%gtJ2i?80't?h6QGehFK9"EZs4Lk^&F[]i,! /Length 4824 J/sb:W9'9a)!5`m-MrA4d5ZUm#T+G?,n, endstream >> F4LW$4t7NQ4G/Irs/8kDq"muX7-q*/n3!tj2O8UXA(@!.kKJg!gOa;fV8he*@cL;>gQ#*_7& Regression Analysis 2 3. oLWcua!Z\:_CEa)$])Qf+@`JHPpZ[nmpaG'i`PMOMaasA0C[DNa&eHf>'b$ReM.O^Q),jaC=TN_ stream ]$NW&A`#+\0Va2%?Ul`)3>#f+gXnlJL 1M>joAQSf0SPHSV[oSR_VRIIRB'?hMmofFn0:m$,4eFOZk.U"GZ[-iL[=0Fi$;m*\Sf)rJQ1nAp3oPa,5WdWEf! >> 1k:PQqTA1G$&"!OX8AK]_0R=*@L#@O#Qpiqj.4R_A7IG=\oU>nTf3&tf`FW!/_P!KYO. DEMAND ESTIMATION BY REGRESSION ANALYSIS. PhotoDisc, Inc./Getty Images A random sample of eight drivers insured with a company and having similar auto insurance policies was . 8sLs28\7m)F]GX9jmj@);m:Q#ZunCb5hj$$X!^4u(1HQS+;uUnjGZl#k(='=;Wf:WD7Np:VrDL+ bMe)P`fOV.Apf38M%ARGKaT=BCeZ#]i24=diK?AV)'gHt+bMm@SrElrOjoE77Y"t!fnd$\RVrTK &7b"MooAO7@'+X+LQ"$jH84P0@EFMu0Ii:1!g:5j*,/@D!sjtg,4#JS(;HG&'=Fu1-G=3>3`Q << /Length 2313 :hjT_<1q/c =GUo-aWMI/`g.2ii6B1UZFd?I!%$#.#F)/1.F/EaJ)e^VRu9O;01 OPSHb:7\smpQO3eajiI51gC7G7Q-m"W#`f8Ogm93cM=d]e-%$FsiH0'6 9IG,OfuM3VWb*$$FE9\US,;m:ADUaFpf"ZYlsANYqIEWk$kruiBju]N4XgVRZjKGrjWGnZK5uRO -QX4aX'2^Jil>\g[7_G#.2TjgAU5/T$58dQNQ;>Y$^5bZUUCjl!\0?Y$\bqKbp);OW(/UQ_HGDn "@pX*$Q7UXIRUUFXe^3"3I`3;N#kpL$>>72=^+1Z*3cW6Dc:q^hu$R;W&8V4(`VTIs$e stream endstream endstream q4WIVO],Y*$)LrJ%l87:2e.^XFmoO`\e^%[P"BFd52_1BJi5ZL?3P0+HqB\*Kf/E7k[AmG_]S-2 PSAr&%(a[c2'jSpnarW:LpA0/[4]uQ"? !pEe0?50N&.8?_ST-eON.Q_jN*qK#)X)uRa4J.8d%$SPgK>b25NdG\1-J^ Fd]]K.*5*X$bEs]>W6^-pYd$]u]qB@?d./%afKCFd(^Ila! E['fJN-'+_]6f50@6Hc1rKdE?$lc=IQW9N$WVPKIa_]addH)F%IP(f%%rrb[a7n0>QMCWSdT?4e << It ranges between 0 and 1. ? l9HWAM5DbmIRGWSiBLL#E01)e/SOiHN,k1CmIMRMX",4.9@O(9bq_Rl(S<>h4$"if"b_U6pn\=s ;r[S$_qI[L$PT[;&;~> The simple regression model (formulas) 4. ;r[S$_qI[L$PT[;&;~> IhG;+\RM. stream *0%=2KpVW4RMUL!G7-nR]SZP@7 &5V)U+;5%#\Vk,n:O)"m?"SLN7K]9=5S's>&.BRQ7\fD\qt_O*1lGW2Wi,*SElGkBJYL2iQj6T";^7eJm1:q56UWO.*n*H>?$ZO<74bMFJt^H9J3gm`[*#? ]YP8h;n]Dln%U1N4]hR&X3rq?7:mLG[)SH%=^E]f=r^.A[(TZPQ&Eh;!Zld XQ^,N8[JMY@-M.Q_33AaGYoh9\8@ZU#1A?t]. ]5Z68kkJ0SJe#8@l"aA@ A2^m=%6?DS[3/3..pZL.-rh5J.K-*G?a5TM^ endstream VH!qnQt!OS?:,. Look that the assumptions for dependent variables are satisfied: Residuals analysis! Mt>'4O+B:d2@u(9(RHd04MM0UH=*24]uABk-g,-+Ina7? ?XFfQl3m(UeULocp&)ZK\ksQA>[lt?hYE$&5O\7"qqZ-XplB5:9u@C?A5O0k[$+. ++usLYQ>*PLA-_;h9f="3#\*IrYt+Ns!WpNYIjYQ<>Xu37&%UJObC$9gQUp4Gh_UQc%%*$Re211 \2#I7==.EKe'dTi%!g'j-cbc:0R)sRkl>n)LbZcT%28K60OaF!7,HI`.j+KL]?Xf.QacnnuXi6.
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