R软件中的主成分分析.docx
样本K”人口密度X"人均耕X”森林IB序号(un2)地面积(ha)乐率(%)1011131415161718192021问题表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开展状况。1呆农业生态经济系统各区域单元的有关数据x“农夫人Xa人均粮露;:黑x”耕地占X，：果园与x»浇灌川均纯收入近食产城(皿，北含;I:地面积比HHlililfeZ占耕地面枳)人)"以m率()比()之比()解答:1模型选择XI：人口密度(人k11)2)XI：森林陵盖率()Xs:人均粮食产量(kg人)X7：耕地占土地面积比率()X9:浇灌田占耕地面积之比()X2:人均耕地面积(ha)X4：农夫人均纯收入(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.其次主成分为Z2,第三主成分为Z3,依次类推，当前m个生成分的累积奉献率到达80%及以上，我们就说脑的大小与前m主成分仃关。并求解转化后的Zi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元相关指标数data.txt(见附录)。在R软件中输入代码：I>TOydato<-read,table(rF:/data,txt,r)I>mydata.pr<-prXncomp(mydavazcorTRUE)I>SUirtnary(mydaca.pr/Ioaciings=TRUE)得到如F结果：3tMaxddeviation2.1!9M2PcopocticaotVaraatce0.517X32CtMlMlYWPgPoCtlea0.517902<cop.:Cc.)ccv<cor3co>.eC4r7c<w<c*p.91.<5SOT4X.02KT00.712333400.5ei001O.45WTT90."61l”70.2329002300.17740<rT4Cy3<ow2<<W3CCc.SCC*tVl0.3"<0.>MVlVJ-O.14«v<VS0.>7<VC0.57>V?0.4>2VV»0.44<O.110.01o.5O.1240.122-0.24<0.9S-o.m-o.>mo.>>>。“，o.i)<.<>>O.IM-0.7l2l，00.2040”7O.20JO.W0.M0.>100.J5。.尔-O.SOOO.SO0.4200.1S40.00-0.1409hB9.Tn。2”9.231-0.2249.1“-4.24<0.3O.CUO.33214S0.1l三D:0.0MJQ27O-OJSOlWO.Q2H01S3O-OKTOWJ0.003C27>0.814R0220.7U>X700.4J05<l0.9221363«0.95*n皿OMS"770.MK<t700.W4M2071.COOOOCOM第生成分的奉献率为乐其次主成分的奉献率为就第三主成分的奉献率为11.6%.前三个主成分的累积奉献率为比另六个主成分可舍去。Zl=O.342X1X2X1XXZ2=X2X1X6Z3=-X2+X从第一主成分中，可看出农业生态经济与人均耕地面积，农夫人均纯收入，人均粮食产量,浇灌田占耕地面积之比，成反比，即人均耕地面积,农夫人均纯收入，人均粮食产量，浇灌田占耕地面枳之比越大，生态农业经济越差。做碎石图：mydata.prCcrrp1Comp2C«rp3COrrP4C<xnp5C<*11>6Comp7Gx118C(XrC»9建立模型：目标变量，农夫人均纯收入（元/人）一yX2：人均耕地面积（ha）xs：人均粮食产量（kg人决策变尤:X1：人口密度（人永m2）X3：森林融盖率（%）X6：经济作物占农作物播面比例(%)X7：耕地占土地面积比率()X8:果园与林地面积之比()X9：浇灌田占耕地面积之比()进展多元线性回来分析：yBo»bix+B?x2+B3×j+Bs×5+Bgx6+B77+B8×b+B9x9在R软件中输入：>attach(wydata)>»ydata.1kf1m(V4-V1+V2+V3+V5÷V6+7+V8+V9:>summary(»ydata.1»)得到以下结果Call:lro(±orUla=V4-Vl+V2÷V3+VS+V6÷V7+V8+V9)Residuals:ninIQMedian3QMax-560.00-143.25-36.29162.19587.24Coefficients:EstimateStd.ErrortvaluePr(>t)(Intercept)-1340.8791259.751-1.0640.308Vl-2.8162.603-1.O20.300V2278.234231.356l2O30.252V325.30915.4551.6380.127V51.7191.5191.1320.280V6-6.30313.798-0.45706S6V727.98963.0640.4440.665V818.96456.572-0.3350.743V952.59339.7811.3220.211Residualstandarderror:319.3on12degreeso£freedomMultipleR-squared:0.6283,AdjustedR-squared:0.3805F-StatiStic:2.535on8and12DF.p-value:0.0710912笈6789此结果不合理，对其做主成分回来检验：Iworcanceofcotoponencs:Co»p.1Cowp.2ComP3Comp.4Comp.5Standarddevifttljn2.15866521.21704971.02031050.606981990.9757460ProportionOfVariance0.58247940.1851512O.13O1Z92O.OH6O53390.0309756CumulativeProportionO582<7940.76763070.89775990.938132609"76082COtnp.6CW.7C04Y.Standerddeviation0.342195310.2129347120.19868227ProportionOtVarianceO.Ol*i637ZO0.0056676I90.00493433CuxnuIeciveProportion0.989398020.9950656701.0000001.oadings:CenBP.1Cowp.2Con.3Comp.4Comp.SCotop.6Covp.7COsriP.8Vl0.344-0.4610.389-0.3240.S840.1210.221V20.7560.SS4-0.3230.114V3-0.Q470.524-0.228-0.671VS0.3740.368-O1660.64?0.S140.103V60.3790.217-0.145-0.644-0.S20.122-0.136V?0.433-0.10O.2S50.131-0.223-0.787-0.223V8-0.130-0.9430.133-0.2270.101V90.446O2420.154-0.2290.50-0.631由结果可得前三个主成分奉献率到达94.4%,然后进展主成分分析:>pre<-predlct(mydaca.br)>11)ydataSzl<-prez1;roydataSz2<-prez2;n)ydavaSz3<-prer3> lro.sol<-ln(V6*zl÷z2zdatwroydatc)> Suninary(lm.sol)Call:Iw(formula三V6*zl+z2,data三ydata)Residuals:MinIQNediein30Hax-7.482-3.465-1.0003.8929.113Coefficients:EstiirateStd.ErrortvaluePr(>t)(Intercept)16.64311.087115.3109.15e-12»*zl3.42000.S0366.7912.32e-06左门z21.96300.89322.1980.0413*Signif.codes:011'0.001110.01%*z0.05、'0.1、Residualstandarderror:4.982onldegreesoffreedomMultipleR-squared:0.7389.AdjustedR-squared:0.7099F-Statistic:25.48on2and18DFzP-value:S.631e-O6在R中建立模型:>wydata.Iin-Iro(V4*V1÷V2÷V3V5÷V6÷V7÷V8÷V9)>Surwnary(mydata.1.ro)Call:lxn(forula=V4-Vl+V2÷V3+VS+V6+V7+V8+V9)Residuals:319.3on12degreesof±reedowNinIQMedian3QMax-560.00-143.25-36.29162.19587.24EstiinateStd.ErrortvaluePr(>c)(Intercept)-1340.8791259.751-1.0640.308Vl-2.8162.603-1.0820.300V2278.234231.3561.2030.252V325.30915.4551.6380.127VS1.7191.5191.132O.2OV6-6.30313.798-0.4570.656V727.98963.06-10.665V8-18.96456.57Z-0.3350.743V9S2.59339.7811.3220.211Coefficients:Residualstandarderror:接着建模:> ydata.1.tn=l(V4-V1+V2+V3+V5÷V6+V7+V9)> 3u11m¾ry(mydta.Im)Call:ln(tormula三V4-Vi+V2+V3+V5+V6+V7+V9)Residuals:MinIQMedian3QKa
