Homework13Dueon2018-06-151.Consideraproblemofmultiplelinearregressioninwhichapatient’sresponseYtoanewdrugBistoberelatedtoherresponseX1toastandarddrugAandherheartrateX2.Supposethat,forallvaluesX1=x1andX2=x2,theregressionfunctionhasaformE(Y)=β0+β1x1+β2x2,andthevaluesof10setsofobservations(xi1,xi2,Yi)aregiventhetablebelow.ixi1xi2yi11.9660.720.862-1.031.164-0.240.161-1.25-0.163-0.164.4703.474.6680.081.6620.895.5683.7103.4662.0(a)Underthestandardassumptionsofmultiplelinearregression,determinethevaluesoftheM.L.E.’sˆβ0,ˆβ1,ˆβ2andˆσ2.(b)Carryoutatestofthefollowinghypotheses:H0:β1=0,H1:β1̸=0.(c)Carryoutatestofthefollowinghypotheses:H0:β2=−1,H1:β2̸=−1.(d)Carryoutatestofthefollowinghypotheses:H0:β1=β2=0H1:ThehypothesisH0isnottrue.1(e)DeterminethevalueofR-square.(f)Findthepredictedvalueandthe95%predictionintervalforapatient’sresponseYtodrugBgiventhatherresponsetodrugAis4andthatherheartrateis65.2
