R软件中的主成分分析

1、表1为某地区农业生态经济系统各区域单元相关指标数据，运用主成分分析方法，用更少的指标信息较为精确地描述该地区农业生态经济的发展状况表1某农业生态经济系统各区域单元的有关数据X1：人口密度 X2：人均耕（人/km2）地面积（ha）YQ：经济作X3-；X4蓝年嘉金潟引渭襄髓：X；S盛:黑年（）/人）人）精忱率（）比（）之比（）（%）11111问题样本序号123456789101112131415161718192021解答:依次类推，当前m个主成分的累积贡献率达到80%及以上，我们就说脑的大小与前m主成分有关。并求解转化后的乙与xj之间的相关系数。2问题解答在F盘保存某地区农业生态经济系统各区域单

2、元相关指标数（见附录）1模型选择X1：人口密度（人/km2）x3：森林覆盖率（%）X5：人均粮食产量（kg/人）X7：耕地占土地面积比率（）X9：灌溉田占耕地面积之比（）x2：人均耕地面积（ha）X4：农民人均纯收入（元/人）X6：经济作物占农作物播面比例（）X8：果园与林地面积之比（）做主成分分析，命名第一主成分为Z1第二主成分为Z2,第三主成分为Z3,在R软件中输入代码：Iinydataread,tablettrF!tKtPf)mydatz-a-prsunmiuy(mydava(prxload!ngs=TRUE)得到如下结果：5 5口E E=的收n n utilutil工CompComp.

3、 .1Camp.1Camp.Z ZCaup,3Caup,3匚口BYiji-TBYiji-T匚口 x.三匚nsp.MCopiji,7nsp.MCopiji,7匚口w wP P.13Caifip-S.13Caifip-SScfijuluddlffvlaLLDnScfijuluddlffvlaLLDn.159921.4451C7.159921.4451C7 fi.71239539D.fi.71239539D.1400114001.41.41抬I I口口上3 3曲口.i i，？，？4b4b 自中工PftlflEbLDBiaPftlflEbLDBia Vtaium0Vtaium0 fil7SNEIfil

4、7SNEI0.0. 毅1 1如1 10i0i ll5BMall5BMa% %056Mg7gBSlLD.aS14Kh53i056Mg7gBSlLD.aS14Kh53i0 0由L*TL*Tg g强0.0030.003 1919。蔺3 3，/ /口熊CwivUtivcCwivUtivc打口口加口口国O O+ +5nSIO3O5nSIO3Ofefe75OC75OC 70Q70Q用4 45 5 561O.561O. 23Dm23Dm。.新73557355：0.#13750.#1375 77Q451M77Q451M训也口.外后】川口口口1 1 叩口L LiHiJ.iHiJ.ln.grln.gr: :鹏1n

5、BfinBfi: :-ii,-ii,1 1Carr*Carr* *CrCrw w.5.5Cmq(Coup.Cmq(Coup.气Comp9Comp9VIVIQ|Q|H2-gH2-g*55&*55&-g.573-Pi-l53-g.573-Pi-l53-43-43vzvz.GL4.GL4口-1-1占主-0-.11D-0-.11DVIVIMMa 例-O.IDJ-O.IDJO.S52O.S52VV4ie-O-ZZfl-O-ZZfl-0_l-0_l -O.14G-O.14G.E3Z.E3Z. .EL3EL3第一主成分的贡献率为,第二主成分的贡献率为,第三主成分的贡献率为。前三个主成分白累积

6、贡献率为,另六个主成分可舍去。Z1=从第一主成分中，可看出农业生态经济与人均耕地面积，农民人均纯收入，人均粮食产量，灌溉田占耕地面积之比，成反比，即人均耕地面积，农民人均纯收入，人均粮食产量，灌溉田占耕地面积之比越大，生态农业经济越差。做碎石图：mydatarCompCompI IComp.2ComaCompSCofnpOComp.TComp3Comp9Comp.2ComaCompSCofnpOComp.TComp3Comp9建立模型：目标变量：农民人均纯收入（元/人）一y决策变量：xi：人口密度（人/km2）x3：森林覆盖率（%）x6：经济作物占农作物播面比例（）X8：果园与林地面积之比（）

7、进行多元线性回归分析：y=B)+Bix+B2x2+B3x3+B5x5+B6x6+B7x7+B8x8+B9x9x2：人均耕地面积（ha）x5：人均粮食产量（kg/人）x7：耕地占土地面积比率（）x9：灌溉田占耕地面积之比（）在R软件中输入:attach(mydara)mydaca,lm=lit(V4V1+VZ+V34V54V6+V7+V6+V9：stut四号匚ya 1 醐得到以下结果Call:liii(foLttiula=V4-UI+V2+V3+V5+V6+V7-bUS-bV9)iResidualstMlnIQMedian3QMaw-560-00-143-25-36.29162.19SB*7.2

8、4CoeffL?ients:EstiimateStd_EcroirtvaluePt(!111彳Intercept)-1340*3791259.7S1-1,0640.306VI-2*8162603-1.0820.300V227B-234231.3E61.3030.253V35.30915.4S51.S350.127V51.7191.5191,1320.280V6-6.30313.79S13.79S-0.457-0.4570 0 55$55$V727,98953,0610.665V8-18-96456,572-0,5350.7T3VS52.52339,7610.211Residualstandar

9、derrct：319.3on12degreescfreedomMultipleR-squsised;,6283rAdjustedR-squsued；,3805Fstatistic;2.535on6and12DF,p-value;0,07109丫=此结果不合理，对其做主成分回归检验：Importanceofcompontrits:Laadinjs:Ccirip.1Coirip.2Comp.3Comp.4Snip.5Compx6Coimp7Comp,RVI0,3440.-1610.369-口.邙0,5B40,1210.E21V20.7SCH554-0.3230.11*1V3一口木70524-0.2

10、28671VS0.3740.368-0.166046470,514.1D3V6口.3790.2170.L4E0,122-.136V?0.433-0.108.2550.131-04223-0.707-0.223VS-0.1300.133-0.227.101790,4460.2420.154-0.229O.SOS-0.631由结果可得前三个主成分贡献率达到,然后进行主成分分析：prewdatazK-jire,1;ift7clac&Sz2-pre,2;ntyd&rz3Im.soK-lm(V6zl+z2dst.a=mydata)summaty(Im.sc1)Standarddeviat

11、iflnPrcpcrtionorvarianceCumulatIveProportionStandariddeviationProportionof:VarianceCumulativeProportionCctnp.12.15ECS52.5B247940.5824794Cctnp.60.3421531.013720a.96S39BO2Comp.21.270497u.iai15iz0.7S75307Comp.31,0203105.L3D1Z9Z0.8977599Ccutip.7L212Q347120.005667S490.955065370Comp.4Comp.S0.eOC981990.497

12、57460o.D4buiJjyu.ujuy40.943313260.9747C082Conip.8a.iees22?0.004934331X0000000在R中建立模型:iny sujiiniry(mydatasujiiniry(mydata Call:lmi(criiiuia=V4-VI+V2+V3+VS+75+V7+VS+V9)继续建模:Coefficients:EsclitiareScd.ErrorrvaluePr(|t|)(Inv&rcepv)16.6311.037115,3109.15e-12*工13.4Z000.5066.7912.32&-06*Z21.96300.

13、893ZZ.1960.0413内Residuals:Residuals:Hi_nLQMedianHi_nLQMedian-7.33-7.337483483L L.口口口Signit.codes:Signit.codes:0 0左舌卡O.ooiO.ooi击击.口.口1 1、士1r口,0505., ,o.o.1RESideals;UinIQMeilicin.3QMax-560.00143.25-36.29162.19587.2Coeficients:EstiraateStd.ErrortvaluePELIt|)(Intercept)-1340.S791259.751-1.0540.30BVI-2.

14、6162.fiCiS-1.0320.300V2273.234231,3561.2Ci3Q.Z5ZV325.30915.4S51.638a,127V51V51.7191.5191.1320.280VG-6.30313.73-0.457a,.6S6V727.98963,064口,444口,665VS-IB,96456.572-0.33S口.743V952.5939.7811.3220.211Residua1standarderror;Residua1standarderror;319.3319.3onon1212decreesdecreesoffoffceedcmceedcmCall：Lm(for

15、mulaV6V6zl+z2rdata30Max3.6933.113Residualstandarderror:4.982R-squared:0.Fst-at-istic：25.45on2and18on18degreescireedcunAdjListedR-squared:0.7099DF.p-value;5-55ie0mydaca.Inn(V4-V1+V2+V3+V5+V6+V7+V9)siunmary(mydaca.Irn)Call:Im(formula=V4-VI+V2+V3+V5+V6+V7+V9)Residuals:MinIQMedian3QMax-552.77-122-93-44.

16、06174.98611.38Coefficients:EstimateStd.ErrortvalueP门旧）(Inveucept)-1313.8931213.498-1.0830.299VI-2.6892.503-1.1540.269VZZ94.636Z16.2671.350O.ZOOV324.64514.7951.6660.120V51.7711.4581.2150.246V6-7.65912.733-0.6010.558V739.60950.8540.7790.450V944.38630.2641.4670.166Residualstandarderror:308.2on13degrees

17、offreedomMultipleR-squared:0.6248,AdjustedR-squarred:0.4228F-statistic:3.093on7and13DF.p-value:.0376wydata.1=Im(V4-VI4-V2+V3+V5+V7+V9)suwwary(wydata.lift)Call:Im(formula=V4-VI+V2+V3+V54-V7+V9)Residuals:IlinIQMedian3QMax-562.72-125.32-59.32152.355mCoefficients;EstimateStd.ErrorcvaluePr(|11)(Intercept

18、)-1583.2331101.840-1.4370.1727VI-2.9422-1.2040.2486V2274.517210.7151.3030.2137V327.99013.395Z.0900.0554.V51.553L.380L.1260.2792V744.33849.0840.9030.3816V945.20329.5371.5300.1482Signif.codes:0、*0.0010.01、才，0.050.1、1Residualstandarderror:301.1on14degreesoffreedomMultipleR-squared:0.6144,AdjustedR-squa

19、red:0.4491F-statistic:3.717on.6and14DF,p-value:0.02013mydata.Lm=Lm(V4-Vl+V2+U3+V5+V9)summary(wdata.Im)Call:Im(formula=V4-vi+V2+V3+V5+V9)Residuals:MinIQMedian3QMax-634.7-138.6-62.6160.6519.9Coefficients:EstimateStd.EuortvaluePr(|r|)(Intercept)-1062.030932.908-1.1380.2728VI-1.8452.108-0.8750.3952V2307

20、.817206.1881.493O.1562V320.60810.5461.9540.0696.V51.7171.3591.2630.2257V943.55629.2991.4870.1578Signif.codes:0十十0.0010.01、畲0.05、.0.1、z1Residualstandarderror:299.2on15degreesoffreedomMultipleR-squared:0.5919#AdjustedR-squared!0.45S8F-statistic:4.3S1on5and15DFZp-value!0.01201mydata.lro=Im(V4-V2+V3+V5+

21、V9)summary(roydata.Im)Call:lw(forwula=V4-V2+V3+VS+V9)Coefficients;Residualstandarderror:297on.16degreesoffreedomMultipleP-squared!0.571,JLdjlistedR-squared!0.4638F-statistic!5.325on4and16DF,p-value:0.006384EsriroaceStd.ErrortvaluePr(|t|)(Intercept)-1396.280844.920-1.6530.1179V2377.319188.8881.9980.0631.V322.07910.3372.136.0485余V52.1731.2461.734.1004V929.76824.5221.2140.