实验11多元及岭回归分析.docx

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

.88000.86757.129087.126935.092673.101060.143213.102207.14