数学建模论文-基于SAS分析我国农村居民家庭消费情.doc

基于SAS分析我国农村居民家庭消费情况的研究一、导言伴随着我国经济的飞速发展，我国已经成为仅次于美国的世界第二大经济体，GDP已经超过德国日本，位居世界第二，人民生活水平有了翻天覆地的改变，但受到金融危机的影响，近几年来物价持续上涨，通货膨胀严重，CPI屡创历史新高，人民的消费能力是否随着GDP的增加而增加了呢？再次我仅以中国统计年鉴-2010中的“农村居民家庭平均每人生活消费支出构成”中的“生活消费总支出”中20002009年的数据为依据利用统计软件SAS进行了相关分析。数据如下：10-25 农村居民家庭平均每人生活消费支出构成单位：%指 标200020032005200720082009生活消费总支出100.00100.00100.00100.00100.00100.00 食品49.1348.5945.4843.0843.6740.97 衣着5.755.725.816.005.795.82 居住15.4715.5814.4917.8018.5420.16 家庭设备用品及服务4.524.324.364.634.755.13 交通通讯5.585.499.5910.199.8410.09 文教娱乐用品及服务11.1811.5811.569.488.598.53 医疗保健5.244.616.586.526.727.20 其他商品及服务3.142.112.132.132.302.112、 分析1，通过对消费种类进行主成分分析判断农村居民家庭的消费情况。2，对主成分标准化后在分析各年的消费能力排名。三、结果猜测1， 农村居民家庭的消费应该主要集中在衣食住行上。2， 农村居民家庭的消费能力并不是随着GDP的增加而增加的。四、数据处理利用SAS软件获取并整理数据，进一步分析数据并得到结果。4.1，导入数据的SAS程序：data zy;input year x1-x8;cards;200049.135.7515.474.525.5811.185.243.14200348.595.7215.584.325.4911.584.612.11200545.485.8114.494.369.5911.566.582.13200743.086.0017.804.6310.199.486.522.13200843.675.7918.544.759.848.596.722.30200940.975.8220.165.1310.098.537.202.11;run;proc corr cov nosimple data=zy;var x1-x8;run;proc princomp data=zy out=aa;var x1-x8;run;data score1;set aa;keep year prin1;proc sort data=score1;by descending prin1;run;proc print data=score1;run;4.2，程序结果如下： The SAS System The CORR Procedure 8 Variables: x1 x2 x3 x4 x5 x6 x7 x8 Covariance Matrix, DF = 5 x1 x2 x3 x4 x1 10.34610667 -0.19080000 -5.78932667 -0.77213333 x2 -0.19080000 0.00963000 0.07444000 0.00749000 x3 -5.78932667 0.07444000 4.73086667 0.61029333 x4 -0.77213333 0.00749000 0.61029333 0.08893667 x5 -6.74865333 0.15148000 2.88947333 0.38264667 x6 3.99022667 -0.06058000 -3.04066667 -0.38685333 x7 -2.95518000 0.05255000 1.39836000 0.21089000 x8 0.75584000 -0.01362000 -0.26518000 -0.01624000 Covariance Matrix, DF = 5 x5 x6 x7 x8 x1 -6.74865333 3.99022667 -2.95518000 0.75584000 x2 0.15148000 -0.06058000 0.05255000 -0.01362000 x3 2.88947333 -3.04066667 1.39836000 -0.26518000 x4 0.38264667 -0.38685333 0.21089000 -0.01624000 x5 5.18926667 -2.31455333 2.16376000 -0.53024000 x6 -2.31455333 2.12014667 -1.07424000 0.15502000 x7 2.16376000 -1.07424000 0.98975000 -0.16134000 x8 -0.53024000 0.15502000 -0.16134000 0.16664000 Pearson Correlation Coefficients, N = 6 Prob |r| under H0: Rho=0 x1 x2 x3 x4 x5 x6 x7 x8x1 1.00000 -0.60447 -0.82750 -0.80494 -0.92103 0.85197 -0.92349 0.57564 0.2037 0.0421 0.0534 0.0091 0.0312 0.0086 0.2319x2 -0.60447 1.00000 0.34876 0.25593 0.67762 -0.42397 0.53827 -0.34000 0.2037 0.4981 0.6245 0.1391 0.4022 0.2706 0.5097x3 -0.82750 0.34876 1.00000 0.94087 0.58317 -0.96010 0.64623 -0.29866 0.0421 0.4981 0.0051 0.2244 0.0024 0.1656 0.5653x4 -0.80494 0.25593 0.94087 1.00000 0.56325 -0.89089 0.71081 -0.13340 0.0534 0.6245 0.0051 0.2445 0.0172 0.1134 0.8011 0.4928 0.1658 0.6598 0.4439 0.0142 0.4495 0.2672 x1 x2 x3 x4 x5 x6 x7 x8x5 -0.92103 0.67762 0.58317 0.56325 1.00000 -0.69780 0.95476 -0.57020 0.0091 0.1391 0.2244 0.2445 0.1232 0.0030 0.2374x6 0.85197 -0.42397 -0.96010 -0.89089 -0.69780 1.00000 -0.74158 0.26080 0.0312 0.4022 0.0024 0.0172 0.1232 0.0915 0.6177x7 -0.92349 0.53827 0.64623 0.71081 0.95476 -0.74158 1.00000 -0.39727 0.0086 0.2706 0.1656 0.1134 0.0030 0.0915 0.4354x8 0.57564 -0.34000 -0.29866 -0.13340 -0.57020 0.26080 -0.39727 1.00000 0.2319 0.5097 0.5653 0.8011 0.2374 0.6177 0.4354 The PRINCOMP Procedure Observations 6 Variables 8 Simple Statistics x1 x2 x3 x4 Mean 45.15333333 5.815000000 17.00666667 4.618333333 StD 3.21653644 0.098132563 2.17505555 0.298222512 Simple Statistics x5 x6 x7 x8 Mean 8.463333333 10.15333333 6.145000000 2.320000000 StD 2.277996195 1.45607234 0.994861799 0.408215629 Correlation Matrix x1 x2 x3 x4 x5 x6 x7 x8x1 1.0000 -.6045 -.8275 -.8049 -.9210 0.8520 -.9235 0.5756x2 -.6045 1.0000 0.3488 0.2559 0.6776 -.4240 0.5383 -.3400x3 -.8275 0.3488 1.0000 0.9409 0.5832 -.9601 0.6462 -.2987x4 -.8049 0.2559 0.9409 1.0000 0.5633 -.8909 0.7108 -.1334x5 -.9210 0.6776 0.5832 0.5633 1.0000 -.6978 0.9548 -.5702x6 0.8520 -.4240 -.9601 -.8909 -.6978 1.0000 -.7416 0.2608x7 -.9235 0.5383 0.6462 0.7108 0.9548 -.7416 1.0000 -.3973x8 0.5756 -.3400 -.2987 -.1334 -.5702 0.2608 -.3973 1.0000 Eigenvalues of the Correlation Matrix Eigenvalue Difference Proportion Cumulative 1 5.53958038 4.26093054 0.6924 0.6924 2 1.27864984 0.60779877 0.1598 0.8523 3 0.67085107 0.26082731 0.0839 0.9361 4 0.41002376 0.30912882 0.0513 0.9874 5 0.10089494 0.10089494 0.0126 1.0000 6 0.00000000 0.00000000 0.0000 1.0000 7 0.00000000 0.00000000 0.0000 1.0000 8 0.00000000 0.0000 1.0000 The PRINCOMP Procedure Eigenvectors Prin1 Prin2 Prin3 Prin4 Prin5 Prin6 Prin7 Prin8x1 -.421195 0.073658 0.071570 -.065309 -.225417 0.870039 0.000000 0.000000x2 0.259714 -.423409 0.640724 -.538493 0.167132 0.111751 -.059057 -.094141x3 0.370540 0.360448 -.162017 -.367816 -.045671 0.122751 0.744369 0.000000x4 0.356312 0.450621 -.049838 0.005869 0.592195 0.292315 -.415392 0.242427x5 0.383433 -.301784 0.108890 0.359780 -.283087 0.155878 0.113669 0.709401x6 -.385975 -.296433 0.000368 0.185556 0.691590 0.031323 0.464713 0.182988x7 0.387261 -.095172 0.138002 0.593253 0.074481 0.248011 0.140164 -.619092x8 -.211937 0.542507 0.724373 0.233698 -.067017 -.207939 0.146121 0.111162Obs year Prin1 1 2009 2.93337 2 2007 1.62394 3 2008 1.42694 4 2005 -0.70866 5 2000 -2.60751 6 2003 -2.668074.3各指标随年份的变化如下图：4.3.1：食品消费总支出随年份的变化图：4.3.2衣着消费总支出随年份的变化图：4.3.3居住消费总支出随年份的变化图：4.3.4家庭设备用品及服务消费总支出随年份的变化图：4.3.5交通通讯消费总支出随年份的变化图：4.3.6文教娱乐用品及服务消费总支出随年份的变化图：4.3.7医疗保健消费总支出随年份变化图：4.3.8其他消费总支出随年份的变化图：4.4，结果分析：利用SAS得到数据的协方差矩阵为：S= x1 10.34610667 -0.19080000 -5.78932667 -0.77213333 x2 -0.19080000 0.00963000 0.07444000 0.00749000 x3 -5.78932667 0.07444000 4.73086667 0.61029333 x4 -0.77213333 0.00749000 0.61029333 0.08893667 x5 -6.74865333 0.15148000 2.88947333 0.38264667 x6 3.99022667 -0.06058000 -3.04066667 -0.38685333 x7 -2.95518000 0.05255000 1.39836000 0.21089000 x8 0.75584000 -0.01362000 -0.26518000 -0.01624000 x1 -6.74865333 3.99022667 -2.95518000 0.75584000 x2 0.15148000 -0.06058000 0.05255000 -0.01362000 x3 2.88947333 -3.04066667 1.39836000 -0.26518000 x4 0.38264667 -0.38685333 0.21089000 -0.01624000 x5 5.18926667 -2.31455333 2.16376000 -0.53024000 x6 -2.31455333 2.12014667 -1.07424000 0.15502000由此看出，各个指标的样本方差差异很大，因此从样本相关系数矩阵出发做主成分分析，得到下面的相关系数矩阵R=1.00000 -0.60447 -0.82750 -0.80494 -0.92103 0.85197 -0.92349 0.57564-0.60447 1.00000 0.34876 0.25593 0.67762 -0.42397 0.53827 -0.34000-0.82750 0.34876 1.00000 0.94087 0.58317 -0.96010 0.64623 -0.29866-0.80494 0.25593 0.94087 1.00000 0.56325 -0.89089 0.71081 -0.13340-0.92103 0.67762 0.58317 0.56325 1.00000 -0.69780 0.95476 -0.570200.85197 -0.42397 -0.96010 -0.89089 -0.69780 1.00000 -0.74158 0.26080-0.92349 0.53827 0.64623 0.71081 0.95476 -0.74158 1.00000 -0.397270.57564 -0.34000 -0.29866 -0.13340 -0.57020 0.26080 -0.39727 1.00000同时得到个样本主成分的贡献率，累计贡献率如下表： Eigenvalues of the Correlation Matrix Eigenvalue Difference Proportion Cumulative 1 5.53958038 4.26093054 0.6924 0.6924 2 1.27864984 0.60779877 0.1598 0.8523 3 0.67085107 0.26082731 0.0839 0.9361 4 0.41002376 0.30912882 0.0513 0.9874 5 0.10089494 0.10089494 0.0126 1.0000 6 0.00000000 0.00000000 0.0000 1.0000 7 0.00000000 0.00000000 0.0000 1.0000 8 0.00000000 0.0000 1.0000 可知第一个前两个主要成分的累积贡献率已经达到了89.08%，或者说农村居民家庭消费支出主要集中在衣食住行上面，下