实验11多元及岭回归分析.docx
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实验11多元及岭回归分析.docx
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实验11多元及岭回归分析
重庆工商大学数学与统计学院
《统计专业实验》课程
实验报告
实验课程:
统计专业实验__
指导教师:
__叶勇____
专业班级:
_统计三班_____
学生姓名:
_黄坤龙__
学生学号:
2012101328____
实验报告
实验项目
实验11多元及岭回归分析
实验日期
2015-6-10
实验地点
81010
实验目的
掌握多元回归模型的变量选择,岭回归分析的思想和操作方法。
实验内容
1.根据数据文件估计北京市人均住房面积的影响模型。
并进行相应分析。
2.建立重庆市人均住房面积的影响模型,根据统计年鉴收集整理指标数据,并进行模型估计和分析。
实验思考题解答:
1.方差膨胀因子VIF的用途和计算公式是什么,其判断标准?
答:
方差膨胀因子是用来诊断一个序列是否存在多重共线性。
自变量xj的方差膨胀因子记为VIF,它的计算方法为:
VIF=1/1-Rj2。
Rj2为以xj为因变量时对其他自变量回归的复测定系数。
VIF越大,表明多重共线性越严重。
当0 实验运行程序、基本步骤及运行结果: 1.根据数据文件估计北京市人均住房面积的影响模型,并进行相应分析。 (1).首先,要确定因变量和自变量,根据题目, 因变量为: 人均住房面积y 自变量为: 人均全年收入x1 人均可支配收入x2 城镇储蓄存款余额x3 人均储蓄余额x4 国内生产总值x5 人均生产总值x6 基本投资额x7 人均基本投资额x8 (2).然后利用SPSS进行多元线性回归分析,得到结果为: 模型汇总b 模型 R R方 调整R方 标准估计的误差 Durbin-Watson 1 .994a .988 .981 .24634 1.681 a.预测变量: (常量),x8,x7,x3,x6,x1,x2,x4。 b.因变量: y 分析: 根据拟合出来的模型可以知道,可决系数为0.988,调整后的可决系数为0.981.说明解释变量解释了被解释变量变异程度的98.1%,进而可以说明模型的拟合效果好。 Anovab 模型 平方和 df 均方 F Sig. 1 回归 59.608 7 8.515 140.325 .000a 残差 .728 12 .061 总计 60.336 19 a.预测变量: (常量),x8,x7,x3,x6,x1,x2,x4。 b.因变量: y 分析: 这是对于模型的整体显著性检验(F检验),根据结果可以看出F检验统计量为140.325,概率P值为0.000<0.05,说明模型通过了显著性检验,模型的拟合是有效的。 已排除的变量b 模型 BetaIn t Sig. 偏相关 共线性统计量 容差 VIF 最小容差 1 x5 10.462a 1.469 .170 .405 1.809E-5 55278.779 1.780E-5 a.模型中的预测变量: (常量),x8,x7,x3,x6,x1,x2,x4。 b.因变量: y 分析: 根据多元线性回归模型的建立,将变量x5排除,它与模型中的其他解释变量存在很严重的多重共线性。 系数a 模型 非标准化系数 标准系数 t Sig. 共线性统计量 B 标准误差 试用版 容差 VIF 1 (常量) 3.964 .241 16.477 .000 x1 .000 .001 -.956 -.817 .430 .001 1361.278 x2 -.001 .001 -2.180 -2.195 .049 .001 980.463 x3 .001 .002 .749 .627 .542 .001 1418.704 x4 .000 .000 -2.480 -2.067 .061 .001 1431.296 x6 .001 .000 5.155 6.301 .000 .002 665.397 x7 3.285E-7 .000 .349 2.505 .028 .052 19.316 x8 .000 .000 .330 .972 .350 .009 114.391 a.因变量: y 分析: 这是对于模型的系数显著性检验(t检验),根据结果可以看出,常数项的P值为0.000<0.05,即是通过了显著性检验;x1的P值为0.43>0.05,没有通过显著性检验;x2的P照顾为0.049<0.05,通过了显著性检验;x3的P值为0.542>0.05,即是没有通过显著性检验;x4的P值为0.061>0.05,没有通过显著性检验;x6的P值为0.000<0.05,通过了显著性检验;x7的P值为0.052>0.05,没有通过显著性检验;x8的P值为0.009<0.05,通过了显著性检验。 再根据方差扩大因子可以看出x1,x2,x3,x4,x6,x8存在多重共线性,只有x7不存在多重共线性。 共线性诊断a 模型 维数 特征值 条件索引 方差比例 (常量) x1 x2 x3 x4 x6 x7 x8 1 1 7.444 1.000 .00 .00 .00 .00 .00 .00 .00 .00 2 .484 3.923 .09 .00 .00 .00 .00 .00 .00 .00 3 .045 12.870 .00 .00 .00 .00 .00 .00 .45 .00 4 .023 18.096 .21 .00 .00 .00 .00 .00 .01 .08 5 .003 48.783 .30 .01 .01 .02 .02 .06 .37 .19 6 .001 99.386 .00 .14 .00 .07 .17 .17 .10 .03 7 .000 144.498 .09 .04 .95 .02 .00 .29 .05 .12 8 .000 239.240 .31 .80 .04 .89 .81 .48 .02 .58 a.因变量: y 残差统计量a 极小值 极大值 均值 标准偏差 N 预测值 5.3141 11.1214 7.8620 1.77123 20 残差 -.41181 .38168 .00000 .19577 20 标准预测值 -1.438 1.840 .000 1.000 20 标准残差 -1.672 1.549 .000 .795 20 a.因变量: y (3).利用岭回归法对模型进行修正 岭回归法就是用过增加一个偏倚量c,使得模型估计更加稳定和显著。 在SPSS中岭回归的实现: 新建一个syntax窗口,调入岭回归语句(引号内为该文件实际所在路径): Include"d: \Ridgeregression.sps". 岭回归命令格式: ridgeregenter=自变量列表 /dep=因变量 /start=c初始值,默认为0 /stop=c终止值,默认为1 /inc=渐进步长,默认0.05) /k=c指定偏倚系数,输出详细回归结果. 最后一定要有一个点. 输入ridgeregenter=x1x2x3x4x6x7x8/dep=y/inc=0.01. 点运行按钮run。 得到结果为: R-SQUAREANDBETACOEFFICIENTSFORESTIMATEDVALUESOFK KRSQx1x2x3x4x6x7x8 ____________________________________________________________________ .00000.98793-.955631-2.18005.748792-2.479815.154638.349141.329859 .01000.94831.378142.176599-.612495-.4981011.173739.185817.140657 .02000.93217.308957.200793-.400480-.301644.779982.112638.242594 .03000.92303.270773.197581-.290430-.203683.608333.085146.273692 .04000.91693.246958.192037-.221381-.143939.510876.073335.282129 .05000.91246.230606.186853-.173260-.103246.447625.068238.281821 .06000.90897.218606.182354-.137464-.073540.403059.066384.277872 .07000.90614.209373.178488-.109634-.050802.369855.066208.272429 .08000.90378.202011.175147-.087294-.032788.344093.066928.266472 .09000.90176.195980.172235-.068922-.018140.323481.068126.260469 .10000.90001.190929.169671-.053524-.005982.306587.069571.254643 .11000.89847.186626.167394-.040419.004278.292467.071127.249094 .12000.89710.182904.165354-.029124.013054.280476.072714.243863 .13000.89588.179646.163513-.019285.020647.270154.074287.238957 .14000.89477.176764.161841-.010636.027280.261166.075818.234368 .15000.89376.174190.160313-.002974.033125.253263.077291.230079 .16000.89283.171875.158908.003862.038311.246253.078698.226069 .17000.89197.169776.157611.009996.042943.239989.080036.222318 .18000.89118.167863.156407.015531.047103.234353.081304.218805 .19000.89045.166108.155285.020549.050859.229252.082503.215509 .20000.88976.164491.154236.025117.054264.224610.083636.212414 .21000.88911.162995.153252.029293.057364.220365.084705.209501 .22000.88850.161603.152325.033124.060197.216467.085713.206756 .23000.88792.160304.151449.036648.062795.212871.086664.204165 .24000.88738.159088.150620.039902.065183.209544.087561.201715 .25000.88686.157946.149833.042913.067386.206453.088407.199395 .26000.88636.156870.149084.045706.069423.203573.089205.197194 .27000.88588.155853.148370.048304.071311.200883.089958.195104 .28000.88543.154890.147687.050725.073064.198362.090669.193116 .29000.88499.153975.147033.052985.074695.195994.091340.191221 .30000.88457.153105.146406.055100.076216.193764.091975.189415 .31000.88416.152276.145802.057082.077637.191660.092574.187689 .32000.88376.151483.145222.058942.078966.189671.093141.186039 .33000.88338.150724.144662.060690.080210.187786.093676.184458 .34000.88301.149997.144122.062336.081378.185997.094183.182944 .35000.88264.149298.143599.063888.082475.184296.094662.181490 .36000.88229.148626.143093.065353.083507.182675.095116.180094 .37000.88194.147979.142603.066736.084478.181130.095546.178751 .38000.88160.147355.142127.068045.085394.179654.095952.177458 .39000.88127.146752.141665.069285.086258.178241.096338.176212 .40000.88095.146169.141215.070460.087073.176889.096702.175011 .41000.88063.145604.140778.071574.087844.175591.097048.173851 .42000.88031.145057.140351.072633.088573.174345.097375.172731 .43000.88000.144526.139936.073639.089263.173148.097685.171648 .44000.87970.144011.139530.074595.089916.171995.097979.170599 .45000.87939.143510.139133.075506.090535.170884.098257.169584 .46000.87910.143023.138746.076373.091123.169813.098520.168600 .47000.87880.142548.138367.077200.091680.168779.098770.167646 .48000.87851.142085.137996.077988.092209.167780.099006.166720 .49000.87822.141634.137632.078740.092711.166813.099229.165820 .50000.87794.141193.137276.079458.093188.165878.099441.164946 .51000.87765.140763.136926.080144.093642.164972.099641.164096 .52000.87737.140342.136583.080799.094073.164094.099830.163269 .53000.87709.139931.136247.081426.094484.163241.100009.162464 .54000.87681.139528.135916.082026.094874.162414.100178.161679 .55000.87653.139133.135591.082599.095245.161610.100337.160915 .56000.87626.138747.135271.083148.095598.160828.100488.160169 .57000.87598.138368.134956.083674.095935.160067.100630.159442 .58000.87571.137996.134646.084178.096255.159327.100763.158732 .59000.87544.137631.134341.084661.096560.158606.100889.158039 .60000.87517.137273.134041.085124.096850.157903.101007.157361 .61000.87489.136921.133745.085568.097126.157217.101118.156699 .62000.87462.136575.133453.085993.097390.156548.101222.156051 .63000.87435.136234.133165.086402.097640.155895.101319.155417 .64000.87408.135900.132881.086793.097879.155257.101410.154796 .65000.87381.135570.132600.087169.098106.154634.101495.154189 .66000.87355.135246.132324.087530.098322.154024.101574.153594 .67000.87328.134926.132050.087876.098527.153428.101647.153011 .68000.87301.134611.131780.088209.098723.152844.101715.152439 .69000.87274.134301.131513.088528.098909.152273.101778.151878 .70000.87247.133995.131250.088835.099086.151713.101836.151328 .71000.87220.133694.130989.089129.099254.151165.101889.150788 .72000.87193.133396.130731.089412.099413.150627.101938.150258 .73000.87166.133102.130476.089684.099565.150100.101982.149738 .74000.87139.132812.130224.089945.099709.149583.102021.149227 .75000.87112.132526.129974.090195.099845.149075.102057.148724 .76000.87085.132243.129727.090436.099974.148577.102089.148230 .77000.87058.131964.129482.090667.100097.148088.102116.147745 .78000.87031.131688.129240.090889.100213.147607.102141.147267 .79000.87004.131415.129000.091102.100322.147135.102161.146798 .80000.86976.131145.128762.091307.100426.146670.102179.146335 .81000.86949.130878.128527.091503.100523.146214.102193.145880 .82000.86922.130614.128294.091692.100615.145764.102203.145432 .83000.86894.130353.128062.091873.100702.145322.102211.144991 .84000.86867.130095.127833.092047.100783.144887.102216.144556 .85000.86840.129839.127606.092213.100860.144459.102218.144128 .86000.86812.129586.127380.092373.100931.144038.102217.143706 .87000.86784.129335.127157.092526.100998.143622.102213.143290 .88000.86757.129087.126935.092673.101060.143213.102207.1
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