R软件中的主成分分析,DOC

1、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样本序号X1：人口密度2 （人/km ）X 2：人均耕地面积（ha）X 3:森林覆 盖率（%）X 4：农民人 均纯收入（元/人）人均粮X 6：经济作 食产人均粮/物占农作物 食产人） （kg/播面比例（% ）X 7：耕地占 土地面积比率（% ）X 8：果园与 林地面积之比（% ）X 9：灌溉田 占耕地面积 之比（% ）1363.9120.35216.101192.11295.3426.72418.4922.23126.

2、2622141.5031.68424.3011 752.35452.2632.31414.4641.45527.0663100.6951.06765.6011 181.54270.1218.2660.1627.47412.4894143.7391.33633.2051 436.12354.2617.48611.8051.89217.5345131.4121.62316.6071 405.09586.5940.68314.4010.30322.932668.3372.03276.2041 540.29216.398.1284.0650.0114.861795.4160.80171.106926.

3、35291.528.1354.0630.0124.862862.9011.65273.3071 501.24225.2518.3522.6450.0343.201986.6240.84168.904897.36196.3716.8615.1760.0556.1671091.3940.81266.502911.24226.5118.2795.6430.0764.4771176.9120.85850.302103.52217.0919.7934.8810.0016.1651251.2741.04164.609968.33181.384.0054.0660.0155.4021368.8310.836

4、62.804957.14194.049.1104.4840.0025.7901477.3010.62360.102824.37188.0919.4095.7215.0558.4131576.9481.02268.0011 255.42211.5511.1023.1330.0103.4251699.2650.65460.7021 251.03220.914.3834.6150.0115.59317118.5050.66163.3041 246.47242.1610.7066.0530.1548.70118141.4730.73754.206814.21193.4611.4196.4420.012

5、12.94519137.7610.59855.9011 124.05228.449.5217.8810.06912.65420117.6121.24554.503805.67175.2318.1065.7890.0488.46121122.7810.73149.1021 313.11236.2926.7247.1620.09210.078解答:1模型选择XI：人口密度（人/km2）X 3：森林覆盖率（%）X 5： 人均粮食产量（kg/人）X 7：耕地占土地面积比率（ ）X 9：灌溉田占耕地面积之比（ ）x 2：人均耕地面积（ha）X 4：农民人均纯收入（元/人）X 6：经济作物占农作物播面比例

6、（ ）X 8：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,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元相关指标数data.txt （见附录）。在R软件中输入代码：|> my data v-(,rF :/dats. txtTr)> mydatapr <- princomp (inydaca, cor = TRUE)> suimnary (mydata pr # loadirigs=TRU

7、E)得到如下结果：Impost nn匚巴 of 匚ojupoocntsiCdonp. 1 Comp 2 Comi j 3 StHJidard deviatlGEi 2.15&.962 :L 4155076 1-021270B P£ apart loti Of ViSiiiee DU5L79D2 0.2321656 0-1156082 CamuliCiiveOd 5L79D2 7500678 0 4659561Camp i. 4 Con>4 5 D.71233508 0.5614001 D.05636027 0a03501S9 00»9573552CeaTTp.

8、 6 CdHQ B7 oarrp8 Campi.9 0J43B877a8 03SB宮X勺些了 0.212900230 17706876 02140153 口Q1210993 .D5D36279 口.00397022 0u97B75677 口9916&70 0b99650Z97S 10000000CIOCcibw > 1C0JUP.2COWCotDp 1 4 Comp.5& CGtnp . 7 Coanp.SVI D342-0.3 6®-D.375 -0.3550.31205590-113-0 .23 3V2! 614D.155 -0.761 -0.110V3 -

9、D.-S46OL£060467 -0.203Q.69ZV4© $!-D.5900.310D.395V5 0 376O.3CT7396 -0L5C8D»58DV6 CL 3790.124 . 1220.200.154D.&38V7一024$-D.146-0.241 -CL 7770.235VS0 950-231W D呵4甫-D12-0.135 -0.2460.532 .613第一主成分的贡献率为51.8%，第二主成分的贡献率为23.2%，第三主成分的贡献率为11.6%。前三个主成分的累积贡献率为 86.6%,另六个主成分可舍去Z1=0.342X1-0.368

10、X2-0.375X4-0.355X5+0.312X6+0.599X7+0.113X8-0.233X9Z2=0.614X2+0.155X4-0.761X5-0.11X6Z3=-0.446X2+0.206X6+0.467X7-0.203X8+0.692X9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：-l “ 一 O CIIIIrIIInComp.1Comp .2Comp 3 Comp .4 Comp 5 Qo

11、nip.Q Comp .7 CompS Cc?mp.g建立模型：目标变量：农民人均纯收入（元/人）一y决策变量：x 2：人均耕地面积（ha）x 5：人均粮食产量（kg/人）xi：人口密度（人/km2）X 3：森林覆盖率（%）x 6：经济作物占农作物播面比例（）x 7：耕地占土地面积比率（ ）X 8：果园与林地面积之比（ ）X 9：灌溉田占耕地面积之比（ ）进行多元线性回归分析：y= B0+B1X+B2X 2+B3X 3+B5X 5+B6X 6+Rx 7+B8X 8+B9X 9在R软件中输入：> attach fmydata）> mydata. lm= lm （V 4 -V1+V2

12、+V3 +V5 +V 5 +V7+V8 +V9:> summary （itiydata* Im）得到以下结果Call!= V4 - U1 + V2 + V3 + V5 + V6 + V7 斗 28 斗 V9JiResiduals:MinIQ Median3QMax-550,00 -143,25-36,25152.1958,24Coefficients:EstimateStd Ecroi：t valuePri( Intercept)-130*3791E59.751-i.ae4匚l308VI-2,316Z, 603-l.aesU 300vz270-234231.3561.203匚 i.252

13、U325-309IS.4551-6330.12?V51*7191.5191,132匚l280V6-6,30313,798-0.457 .6S6V763.ae40-444D.66EU8-1S-96456.572-0-2350.?43V9S2*59339.7811.322口 211Fesldual standacd errcu: 3193 on 12 degrees o± freedomMultiple R-squsced; 6283,Adjusted R-squsued; 3805F-statistic; 2on 6 and 12 DF, p-value; 0*07109y=-1340

14、.879-2.816X 1+278.234X2+25.309X3+1.719X5-6.303X6+27.989X7-18 .964X8+52.593X9此结果不合理，对其做主成分回归检验：Impartance of coixipcnents:S t andar d dev i at iQn.Proportion of Varlance Cumulative ProportionComp -12.15866520.5S247940582794Comp. 21.21704970.18515120.7676307Comp. 31.02031050.13 口他 2 0.8977599Comp-4 .

15、6069S1990.04605339 .9138132650.497S7460 0.03094756 CL 97476062Standard deviation. Proportion of Variance Cumulative ProportionComp + 6O.34219S31 0.01463720 0.989390020.2129347120.0056676490,995 口逝 7©Comp.S0.19S682270.00493433 1>00000口口口Loadings:Comp. 1Comp. 2Ccmp* 3Camp T 4Cotnp * SCctnp. 6C

16、omp,7Cotnp, 8VI0.3,-Oh 4610.389-0.3240,580.1210.221V20.756 .554 .114V3-0.44?0.S24-228-.671V50.3 740,368-0.1660, 6470.S140.103V60*3790,217-0.145-D心4-0*5320. 1227,13 6V7D*侏-0.103U 255 . 131-0,2237 787-口*223V8-0.130-0.9430.133-口227. 101V90,4460,2420, 154-0.229 508-0.631由结果可得前三个主成分贡献率达到94.4%,然后进行主成分分析：&

17、gt; pre<-predictmydatabr)> mydata$ zK-pre / 1 ； mydataS z2 <-pre f2 ;raydata$ s3<-pre f 3> Ini. sol<-lm (V6«zl+z2 f data=myciat-a)> s ummary(lm * so1)Call:data - itiydara)liti (formula = V6 zl + z.2 fResiduals:3Q Max3.0929,113HinIQ Median-7.482 -3,465 -1,000Coeffic rents:Es

18、timate Std,Euror t value Pr(>|t|)(Intercept) z 116.64313*420096301口B7115310m15e-120.5036CL 093 26.791 2.32e-062.1980,013 卞S ignif.匚口des:W 0.05Residual standard error: 4.5S2Multiple R-squared: 0*73B9F-statistic: 35,48 on 2 and 18on 1C degrees of ft:亡AdjU3ted R-squared: 7099DF, p-value: 5,63le-06在R

19、中建立模型:> mydata. lm=lm (V4-V1+V2 +V3 +VS+V6+V7+V6+V9> s uramar y roydata. lxn)Call:+ V7 + V© + V9JLm(formula = Vl * VI + V2 + V3 + V5 + V6Residuals :MinIQ Median3Q Hax-560.00 -14325 3629 162.19 587.24Coeff icients i：Est iinateStd Errort valuePr(>|c|)（In匸己匸u亡p匸）-1340*8791259.751-1064303V

20、I-2,0162,603-1.0S203MV2278九231.3561.2 03 .252V325.309仅4551.638 127VS1,7191.5191.1320,280V6一&30313.798-0.457» 65 6V727.98963.064 .444 665V8-IS.96456.572-口. 3350.743V952.59339.7S11.3220.211Residual standard error: 319.3 on 12 degrees of freedom继续建模:> mydata.lm=lm(V4-V1+V2 +V3 +V5 +V6 +V7 +

21、V9)> summary(mydatalm)Call:lm(formula = V4 - VI + V2 + V3 + V5 + V6 + V7 + V9)Residuals:MinIQ Median3QMax-552.77 -122.93-44.06174.98611.38Coefficients:EstimateStd. Errort valuePr(>|t|)(Intercept)-1313.8931213.498-1.0830.299VI-2.8892.503-1.1540.2 69V2294.636218.2671.3500.200V324.64514.7951.6660

22、.120V51.7711.4581.2150.246V6-7.65912.733-0.6010.558V739.60950.8540.7790.450V944.38630.2641.4670.166Residual standard error: 308.2 on 13 degrees of freedomMultiple R-squared: 0.6248,Adjusted R-squared: 0.4228F-statistic: 3.093 on 7 and 13 DFX p-value: 0.0376> mydata.lm=lm(V4-V1+V2 +V3 +V5 +V7 +V9)

23、> suwonary (mydata. Im)Call:lm(formula = V4 - VI + V2 + V3 + V5 + V7 + V9)Residuals:MinIQ Median3QMax0.01 * 0.050.1562.72 -125.32-59.32152.35542.44Reis i dualstandard error:301.1 on 14 degrees of freedomMultiple R-squared: 0.6144,Adjusted R-squared: 0.4491EstimateStd Errort valuePr(>|t|)(Inter

24、cept)-1583.2331101.840-1.4370.1727VI-2.9422.444-1.2040.2486V2274.517210.7151.3030.2137V327.99013.3952.0900.0554 V51.5531.3801.12 60.2792V744.33849.0840.9030.3816V945.20329.5371.5300.1482Coefficients:Signif. codes:00.001F-statistic: 3.717 on 6 and 14 DFZ p-value: 0.02013> mydata. lm=lm(V4-Vl +V2 +

25、V3 +V5 +V9)0.001、" 0.01、朴 0.05、 0.1> sununary (mydata. Im)Call:lm(formula = V4 - VI + V2 + V3 + V5 + V9)Residuals:MinIQ Median3QMax-634.7 -138.6-62.6160.6519.9EstimateStd. Errort valuePr(>|t|)(Intercept)-1062.030932.908-1.1380.2728VI-1.8452 108-0.8750.3952V2307.817206.1881.49301562V320.60

26、810.5481.9540.0696 .V51.7171.3591.2 630.2257V943.55629.2991.4870.1578Coefficients:Signif. codes:Q 、K 我 *，Residual standard error: 299.2 on 15 degrees of freedom Multiple R-squared: 0.5919,Adjusted R-squared: 0.4558F-statistic: 4.351 on 5 and 15 DF, p-value: 0.01201> inydata. ln)=ln)(V4-V2+V3+V5+V

27、9)> suimiary (mydata. Im)Call:lm(formula = V4 - V2 + V3 + V5 + V9)Residuals:MinIQ Median3Q Max-589.93 -135.27-9.73188.00535.86Coefficients:EstimateStd. Errort valuePr(>|t|)(Intercept)-1396.280844.920-1.6530.1179V2377.319188.8881.9980.0631 V322.07910.3372.13 60.0485 *V52 1731.2461.7440.1004V929.76824.5221.2140.2424Signif. codes: 00.0010.01 、仪 0.05 、 0.1 、 z 1Residual standard error: 297 on 16 degrees of freedomMultiple R-squared: 0.571,Adjusted R-squared: 0.4638F-statistic: 5.325 on 4 &nd 16 DFZ p-value: 0.006384> itiydaca, lm= ln(V4V2+V3+V5)> suBmia