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1、Chapter11:LinearModelsandEstimationbyLeastSquaresK11.1Usingthehint,yˆ(x)=βˆ+βˆx=(y−βˆx)+βˆx=y.011111.2a.slope=0,intercept=1.SSE=6.b.Thelinewithanegativeslopeshouldexhibitabetterfit.c.SSEdecreaseswhentheslopechangesfrom.8to.7.Thelineispivotingaroundthepoint(0,1),andthisisc
2、onsistentwith(x,y)frompartEx.11.1.d.Thebestfitis:y=1.000+0.700x.11.3Thesummarystatisticsare:x=0,y=1.5,Sxy=–6,Sxx=10.Thus,yˆ=1.5–.6x.p11.3y0.51.01.52.02.53.0-2-1012p11.3xThegraphisabove.11.4Thesummarystatisticsare:x=72,y=72.1,Sxy=54,243,Sxx=54,714.Thus,yˆ=0.72+0.99x.Whenx=
3、100,thebestestimateofyisyˆ=0.72+0.99(100)=99.72.11.5Thesummarystatisticsare:x=4.5,y=43.3625,Sxy=203.35,Sxx=42.Thus,yˆ=21.575+4.842x.Sincetheslopeispositive,thissuggestsanincreaseinmedianpricesovertime.Also,theexpectedannualincreaseis$4,842.11.6a.intercept=43.362,SSE=1002.
4、839.b.thedatashowanincreasingtrend,soalinewithanegativeslopewouldnotfitwell.c.Answersvary.d.Answersvary.e.(4.5,43.3625)f.ThesumoftheareasistheSSE.211.7a.Therelationshipappearstobeproportionaltox.b.No.c.No,itisthebestlinearmodel.230Chapter11:LinearModelsandEstimationbyLeas
5、tSquares231Instructor’sSolutionsManual11.8Thesummarystatisticsare:x=15.505,y=9.448,Sxy=1546.459,Sxx=2359.929.Thus,yˆ=–0.712+0.655x.Whenx=12,thebestestimateofyisyˆ=–.712+0.655(12)=7.148.11.9a.Seepartc.b.yˆ=–15.45+65.17x.p11.9y60801001201401.61.82.02.22.4p11.9xc.Thegraphisa
6、bove.d.Whenx=1.9,thebestestimateofyisyˆ=–15.45+65.17(1.9)=108.373.ndSSEnn2ˆ∑i=1xiyi.11.10dβ=−2∑i=1(yi−β1xi)xi=−2∑i=1(xiyi−β1xi)=0,soβ1=n21∑xi=1inn2βˆ=2.514.11.11Since∑i=1xiyi=134,542and∑i=1xi=53,514,111.12Thesummarystatisticsare:x=20.4,y=12.94,Sxy=–425.571,Sxx=1859.2.a.Th
7、eleastsquareslineis:yˆ=17.609–0.229x.232Chapter11:LinearModelsandEstimationbyLeastSquaresInstructor’sSolutionsManualp11.12y082614121018101020304050p11.12xb.Thelineprovidesareasonablefit.c.Whenx=20,thebestestimateofyisyˆ=17.609–0.229(20)=13.029lbs.11.13Thesummarystatistics
8、are:x=6.177,y=270.5,Sxy=–5830.04,Sxx=198.29.a.Theleastsquareslineis:yˆ=452.119–29.402x.p11.13y20
