R软件中的主成分分析报告.docx

1、R软件中的主成分分析报告问题表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址八 A n 如E W 农民人XS：人均粮:誓篦X7：耕地占g 果园与X9:灌溉田梓本X】：人口密X2：人均耕X?：森林復阳姉一彳 令各二 物占农作物r Wir?n-toMz廿抽侖士甜殆滴知 Q 口 rfr/ A /I 2 riTt frt/1 士 八 均纯收入（元 貝产量 .we _u a-. 土地面枳比林地面枳之占耕地面积序号度（人/km?）地面积（1识）盖率（） . . . n ,. 播

2、面比例 如“八 亠“八 亠/ 人） （kg/人） （） 率（） 比（） 之比（）1363.9120.35216.101192.11295.3426.72418.4922.23126.2622141.5031.68424.3011 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 405.09586.5940.683

3、14.4010.30322.932668.3372.03276.2041 540.29216.398.1284.0650.0114.861795.4160.80171.106926.35291.528.1354.0630.0124.862862.9011.65273.3071 501.24225.2518.3522.6450.0343.201986.6240.84168.904897.36196.3716.8615.1760.0556.1671091.3940.81266.502911.24226.5118.2795.6430.0764.4771176.9120.85850.302103.52

4、217.0919.7934.8810.0016.1651251.2741.04164.609968.33181.384.0054.0660.0155.4021368.8310.83662.804957.14194.049.1104.4840.0025.7901477.3010.62360.102824.37188.0919.4095.7215.0558.4131576.9481.02268.0011 255.42211.5511.1023.1330.0103.4251699.2650.65460.7021 251.03220.914.3834.6150.0115.59317118.5050.6

5、6163.3041 246.47242.1610.7066.0530.1548.70118141.4730.73754.206814.21193.4611.4196.4420.01212.94519137.7610.59855.9011 124.05228.449.5217.8810.06912.65420117.6121.24554.503805.67175.2318.1065.7890.0488.46121122.7810.73149.1021 313.11236.2926.7247.1620.09210.0781模型选择X1：人口密度（人/Ion2）X3：森林覆盖率（）X5：人均粮食产量

6、（kg/A）Xg：灌溉田占耕地面积之比（）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厂之间的相关系数。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:wydata mydata.pi: suirmary (mydat-a. pr； Loadings=TRUE)得到如下结果：JjnpoxtaDce oi Gonponeats: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

7、成分的贡献率为11.6%o前三个主成分的累积贡献率为86.6%,另六个主成分可 舍去。Zl=0.342Xl-0.368X2-0.375X4-0.355X5+0.312X6+0.599X7+0.113X8-0.233X9Z2=0.614X2+0.155X4-0.761X5-0.11X6Z3=-0.446X2+0.20GX6+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:mydata.pr

8、建立模型：目标变量：农民人均纯收入（元/人）一y决策变:X2:人均耕地面积（hx5：人均粮食产量（1毎/人）x7:耕地占土地面积比率（）X9：灌溉田占耕地面积之比（）X1：人口密度（人/km）x3：森林覆盖率（）XC：经济作物占农作物播面比例（）X3:果园与林地面积之比（）进行多元线性回归分析：y= Bo+B1x+B2x 2+BoX 3+B5x 5+B6x g+B7x 7+B8 x g+B9x 9在R软件中输入:rnydata lrn= lm (V4-V1+V2 +V3 +V5+V6+V7+V8+V9:surmtiaxzy (roydata. lrn)得到以下结果Call:lm(formula

9、 = V4 - VI + U2 + V3 + V5 + V6 + V7 + V8 + V9)Residuals:Min IQMedian3QMax-560.00 -143.25-36.29162.19587.24Coefficients:Es匚imateStd. Error匚 valuePr(Intercept)-1340.8791259.751-1.0640.308VI-2.8162.603-1.0820.300VZZ78.234231.3561.2030.252U3Z5.30915.4551.6380.127U51.7191.5191.1320.280U6-6.30313.798-0.45

10、?0.656V727.98963.0640.4440.665U8-18.96456.572-0.3350.743U952.59339.7811.3220.211Residual standard e匚匚ou: 319.3 on 12 degrees o freedomMui匚ipie R-squared: 0.6283 Adjusted R-squared: 0.3805F-statis匚ic; 2.535 on 8 and 12 DF， p-value: 0.07109y=-1340.879-2.816X1+278.234X2+25.309X3+1.719X5-6.303X6+27.989X

11、7-18.964X8+52.593X9此结果不合理，对其做主成分回归检验:Importance of components:Loadings:Coirip 1Comp 2Cornp 3Comp 4Comp 5Comp 6Comp 7Comp 8VI0.344-04610 389-03240.5840 1210.221V20 7560 554-03230 114V3-04470.524-0228-0 671V50 3740.3 68-0.166Cl 6470.514Cl 103V60 3790.217-0145-0 644-05820 122-0 13 6V70 433-01080.255Cl

12、131-0.223-0787-0223V8-0130-0.9430.133-02270.101V90 4460 2420 154-0.2290.508-0 631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:premydata$zl-pre , 1 ; myd&t&$ z2-pre/.2 ;mydata$z3wydara 1如 Lm CV4i+V2+V3+V3+V6+V7+V8+smruriary (itiydata lit)Call；lw(orwula = V4 - VI + V2 + V3 + V5 + V6 十 W?十 V8 十 V9)Residuals;Ilin IQ

13、 Median. 3Q Maxdegrees of freedom-5 6000 -14325 -3 629 162 19 5872址EstimateStd. Errort. valuePr(|t|)(Intercept)1340.8791259 75：L:L 0640.3CI8VI2 8162 603:L 0320.30CIV2278.234231.356L.2O30 252V325.30915455:L 63 80 127VS1 7191 519:L13 20 280V6-6.30313 798-04570 656V?27.98963 06404440 665V8-18.96456572-

14、03350 743V9S2 593397811.3220 211Coefficients:Residual standard error:319.3 on 12继续建模:mydata. Lm= lrti (V4-V1+V2 +V3 +V5+V6 +V7 +V9)suinmary (rriydata. Im)Call:lm(formula = V4 - VI + V2 + V3 + V5 + V6 + V7 + V9)Residuals:Min-55277 -122IQ Median.93 -44.06301=49吕Max611.38Coef f icient-sEstimate Std Err

15、ort valuePr(|t|)(Inve匚ezp匸)-1313.8931213.438-1.0830.299VI-2.8892.503-1. 1540.2 69VZ294.6362 18.2671.3500.200V324.6451吆7951 6660 120V51.7711 4581.2150 246V6-7.65912.73306010 558V739.609508540 7790 450V944.386302641 4670 166Residual standard etrtror: 308 2 on 13 degrees of freedomMultiple R-squared: 0

16、6248f Adjusted R-squared: 0.4228F-statistic: 3-093 on ? and 13 DFwydat lx产 1 尚suwtrtary (wydata Lm)Call:lrn (formula = V4 - VI + V2 + V3 + V5 + U? + U9)Residuals:Kin IQ Median. 3Q Max-562.72 -125.32 -59.32 152.35 542.44Coefficients:EstimateStd. Error匚 valuePrOlcn(Intercept)-1583.2331101&址0-:L 4370.1

17、727VI-2 9422 4:44-:L 200.2486V2274.517210.7L5:L 3030.2137V327990L3 3952 0900.0554 V51.5531 3 801 1Z60.2792V744.338490840 9030.3816V945.20329537:L 5300.1482Signif codes: 0 、*e 0 001 、* 001. 0.05 、 * 0.1 、 1 standard error: 3 01 1. on 14 degrees of freedomR-squar ed : 0 6144 Adjusted Rsquerrgd: 0 4491

18、F-stat is tic: 3 717 on. 6 and 14 DFZ p-value: 0.02013rnydata surcanary tmvdata, lrn)Call:lm(formula = V4 - VI + U2 + V3 + V5 + V9)Residuals:Min IQ Median 3Q Max一634 7 一1_38 6 -62.6 160.6 519 9Coefficients:EstimateStd. Errort valuePr(|t|)(Intercept)-1062.03Q932.903-1.1360.2728VI-1.8452.108-0.8750.39

19、52V2307.817206.1881.4930.1562V320.60810.5481 95400696V51.7171.3591 2 6302257V943.55629.2991 4870 1578Signlf codes: 0 *汁汁汁 0.001 卞/ 001 、需005 01 1Residual standard error: 299.2 on 15 degrees o freedoinMultiple R-squared: 0.5919x Adjusted P-squared: 04558F-statistic: 4351 on 5 and 15 DF, p-value: 0.01

20、201mydatalw=lw(V4-V2+V3+V5+V9)3urt(raary (inydata ln)Call!lw(orwula = V4 - V2 + V3 + V5 + V9)Residuals:Min 10 Median 3Q Max-58993 -13S27 -973 18800 53586Coefficients;EstimateStd. Errort valuePr(|t|)(Intercept)-1336.280844.920-1.653.1179V2377.319188.8881.9980.0631 .V322.07910.3372.13 60.0485 *V52 173

21、1.24617址址01004V92976824.5221 2 14024245igni codes: 0 0.001 n 00：L 、畜005 0.1 * 1Residual standard error: 297 on. 16 degrees of freedomMultiple P-squared: 0571, Adjusted R-squared: 04638F-statistic: 532S on 4 and. 16 DF, p-value: 0006384wydata. lm= lw (V4 -V2 +V3 +VS)simiwary (mydata lm)Call:lw(forwul

22、a = V4 - V2 + V3 + V5)Pes iduals:Min iQ Hedian 3Q Max0.05 0.1 、-749合S -i4249 i436 2SOS3 4755仔Coeicients;EstimateStd. Error t. value Pr (| 匚I)(Intercept)-613.453553.459-1.1080.2831V2382 723191址98:L 99900618 V312.0256 271L 91800721 V52 458L 2 4:1:L 98000641 Signi codes:0 、古古古0 001 n CLOL w此结果结果符合要求c作图得Fitted valueslm(V4 V2 十 V3 + V5)Normal Q-Qcnronp 一 S(DP(DZ 一 Eropuss2 10 12Theoretical Quantileslm(V4 - V2 + V3 + V5)Scale-LocationFitted valueslm(#4 V2 十 V3 十站5)Residuals vs Leverage0.0 0.1 0.2 0.3 0.4 0.5 0.6Leveragelm(V4 V2 + V3 + V5)所以回归方程为:y613.453+382.723X2+12.025X3+2.458X5