回归分析.docx
《回归分析.docx》由会员分享，可在线阅读，更多相关《回归分析.docx（26页珍藏版）》请在冰豆网上搜索。
回归分析
应用回归分析
习题9.3：
（1）程序：
datals;
inputxy;
x1=1/x;
y1=log（y）;
cards;
4.20.086
4.060.09
3.80.1
3.60.12
3.40.13
3.20.15
30.17
2.80.19
2.60.22
2.40.24
2.20.35
20.44
1.80.62
1.60.94
1.41.62
;
procregdata=ls;
modely1=x1/r;
plotstudent.*p.='*';
run;
非线性回归思想：
有许多回归模型的被解释变量y与x之间不是线性关系，其中一些回归模型可以通过自变量和因变量的变换转化为线性关系，利用线性回归的求解方法求解。
残差图：
程序结果：
P值小于0.05，可以认为回归方程显著。
参数分别为-3.856和6.08由此方程为
（2）对于加性误差项不能通过取对数的方式求解，只能用非线性的方式估出要求的值。
程序：
datals;
inputxy;
cards;
4.20.086
4.060.09
3.80.1
3.60.12
3.40.13
3.20.15
30.17
2.80.19
2.60.22
2.40.24
2.20.35
20.44
1.80.62
1.60.94
1.41.62
;
procnlin;
parametersa=1b=0.5;
modely=a*exp（b/x）;
run;
SAS系统2009年09月28日星期一下午04时14分37秒6
TheNLINProcedure
DependentVariabley
Method:
Gauss-Newton
IterativePhase
Sumof
IterabSquares
01.00000.500012.6462
10.24791.48171.5534
20.12732.49601.0435
30.04763.86240.9899
40.02675.05320.5526
50.01856.22970.00684
60.02136.05280.00158
70.02136.06060.00121
80.02136.06050.00121
NOTE:
Convergencecriterionmet.
EstimationSummary
MethodGauss-Newton
Iterations8
Subiterations5
AverageSubiterations0.625
R4.075E-7
PPC（a）4.129E-8
RPC（b）9.49E-6
SAS系统2009年09月28日星期一下午04时14分37秒7
TheNLINProcedure
EstimationSummary
Object4.332E-6
Objective0.001206
ObservationsRead15
ObservationsUsed15
ObservationsMissing0
NOTE:
Aninterceptwasnotspecifiedforthismodel.
SumofMeanApprox
SourceDFSquaresSquareFValuePr>F
Model24.45762.228824029.3<.0001
Error130.001210.000093
UncorrectedTotal154.4588
Approx
ParameterEstimateStdErrorApproximate95%ConfidenceLimits
a0.02130.0006210.02000.0227
b6.06050.04455.96456.1566
SAS系统2009年09月28日星期一下午04时14分37秒8
TheNLINProcedure
ApproximateCorrelationMatrix
ab
a1.0000000-0.9876251
b-0.98762511.0000000
从结果看出a,b的估计值分别为0.0213和6.0605
9.4
（1）
非线性回归思想：
有许多回归模型的被解释变量y与x之间不是线性关系，其中一些回归模型可以通过自变量和因变量的变换转化为线性关系，利用线性回归的求解方法求解。
程序：
dataowe;
inputty@@;
y1=log（1/y）;
cards;
17.529.8311.4413.3517.2620.6729.1834.6
947.41055.51159.61262.21366.51472.71577.2
1682.41785.41886.81987.2
;
procregdata=owe;
modely1=t/r;
run;
结果：
SAS系统2009年09月28日星期一下午10时03分27秒1
TheREGProcedure
Model:
MODEL1
DependentVariable:
y1
NumberofObservationsRead19
NumberofObservationsUsed19
AnalysisofVariance
SumofMean
SourceDFSquaresSquareFValuePr>F
Model111.5109911.51099179.50<.0001
Error171.090170.06413
CorrectedTotal1812.60117
RootMSE0.25323R-Square0.9135
DependentMean-3.62196AdjR-Sq0.9084
CoeffVar-6.99166
SAS系统2009年09月28日星期一下午10时03分27秒2
TheREGProcedure
Model:
MODEL1
DependentVariable:
y1
ParameterEstimates
ParameterStandard
VariableDFEstimateErrortValuePr>|t|
Intercept1-2.200870.12094-18.20<.0001
t1-0.142110.01061-13.40<.0001
SAS系统2009年09月28日星期一下午10时03分27秒3
TheREGProcedure
Model:
MODEL1
DependentVariable:
y1
OutputStatistics
DependentPredictedStdErrorStdErrorStudentCook's
ObsVariableValueMeanPredictResidualResidualResidual-2-1012D
1-2.0149-2.34300.11180.32810.2271.444||**|0.252
2-2.2824-2.48510.10280.20270.2310.876||*|0.076
3-2.4336-2.62720.09430.19360.2350.824||*|0.055
4-2.5878-2.76930.08620.18150.2380.762||*|0.038
5-2.8449-2.91140.07870.06650.2410.276|||0.004
6-3.0253-3.05350.07190.02820.2430.116|||0.001
7-3.3707-3.19560.0662-0.17510.244-0.716|*||0.019
8-3.5439-3.33770.0618-0.20610.246-0.839|*||0.022
9-3.8586-3.47980.0591-0.37880.246-1.538|***||0.068
10-4.0164-3.62200.0581-0.39440.246-1.600|***||0.071
11-4.0877-3.76410.0591-0.32360.246-1.314|**||0.050
12-4.1304-3.90620.0618-0.22420.246-0.913|*||0.026
13-4.1972-4.04830.0662-0.14890.244-0.609|*||0.014
14-4.2863-4.19040.0719-0.09600.243-0.395|||0.007
15-4.3464-4.33250.0787-0.01390.241-0.0578|||0.000
16-4.4116-4.47460.08620.06300.2380.265|||0.005
17-4.4473-4.61670.09430.16940.2350.721||*|0.042
18-4.4636-4.75880.10280.29520.2311.276||**|0.161
19-4.4682-4.90090.11180.43270.2271.904||***|0.438
SAS系统2009年09月28日星期一下午10时03分27秒4
TheREGProcedure
Model:
MODEL1
DependentVariable:
y1
SumofResiduals0
SumofSquaredResiduals1.09017
PredictedResidualSS（PRESS）1.40920
分析如下：
由估计值的检验p值均小于0.05，可以得到结论回归方程显著，由
的估计值可以得到线性回归方程
（2）
程序
procnlindata=ls;
modely=1/（1/u+b0*b1**t）;
parametersu=100b0=1b1=0.5;
run;
SAS系统2009年09月28日星期一下午09时41分35秒7
TheNLINProcedure
DependentVariabley
Method:
Gauss-Newton
IterativePhase
Sumof
Iterub0b1Squares
0100.01.00000.50001649.9
197.92500.56620.53661400.6
291.43970.10060.63321135.3
386.37020.12060.7753114.3
489.52350.15660.73132.1923
590.92050.16640.73240.00140
690.93400.16710.73214.357E-8
790.93390.16710.73215.68E-18
NOTE:
Convergencecriterionmet.
EstimationSummary
MethodGauss-Newton
Iterations7
Subiterations3
AverageSubiterations0.428571
R1
PPC1.6E-10
RPC（b0）0.000013
Object0.041754
SAS系统2009年09月28日星期一下午09时41分35秒8
TheNLINProcedure
EstimationSummary
Objective5.68E-18
ObservationsRead3
ObservationsUsed3
ObservationsMissing0
SumofMeanApprox
SourceDFSquaresSquareFValuePr>F
Model39092.83030.9..
Error05.68E-18.
CorrectedTotal22809.0
Approx
ParameterEstimateStdErrorApproximate95%ConfidenceLimits
u90.9339...
b00.1671...
b10.7321...
由结果可得b0b1的值，分别为0.16710.7321
9.5
程序：
datals;
inputtcpigdpkl;
y=log（gdp）;
x1=log（k）;
x2=log（l）;
cards;
11003624.11377.940152
2101.93962.91446.741024
3109.544124.21451.542361
4112.284330.61408.143725
5114.534623.11536.945295
6116.825080.21716.446436
7119.975977.32057.748197
8131.136836.32582.249873
9139.657305.4275451282
10149.857983.22884.352783
11178.028385.93086.854334
12210.068049.72901.555329
13216.578564.32975.464749
14223.949653.53356.865491
15238.2711179.94044.266152
16273.29126735487.966808
17339.1613786.9567967455
18397.1514724.3601268065
19430.1215782.86246.568950
20442.1616840.6643669820
21438.6217861.66736.170637
22432.4818975.97098.971394
23434.2120604.77510.572085
24437.25222568567.373025
25433.75242479764.973740
;
procregdata=ls;
modely=x1x2/rdwvif;
run;
SAS系统2009年09月28日星期一下午09时41分35秒9
TheNLINProcedure
ApproximateCorrelationMatrix
ub0b1
u...
b0...
b1...
SAS系统2009年09月28日星期一下午09时41分35秒15
TheREGProcedure
Model:
MODEL1
DependentVariable:
y
NumberofObservationsRead25
NumberofObservationsUsed25
AnalysisofVariance
SumofMean
SourceDFSquaresSquareFValuePr>F
Model28.445644.222821805.49<.0001
Error220.051460.00234
CorrectedTotal248.49710
RootMSE0.04836R-Square0.9939
DependentMean9.15170AdjR-Sq0.9934
CoeffVar0.52845
SAS系统2009年09月28日星期一下午09时41分35秒16
TheREGProcedure
Model:
MODEL1
DependentVariable:
y
ParameterEstimates
ParameterStandardVariance
VariableDFEstimateErrortValuePr>|t|Inflation
Intercept1-1.785451.43848-1.240.22760
x110.801070.0557514.37<.000113.03374
x210.401640.170592.350.027913.03374
SAS系统2009年09月28日星期一下午09时41分35秒17
TheREGProcedure
Model:
MODEL1
DependentVariable:
y
Durbin-WatsonD0.715
NumberofObservations25
1stOrderAutocorrelation0.594
SAS系统2009年09月28日星期一下午09时41分35秒18
TheREGProcedure
Model:
MODEL1
DependentVariable:
y
OutputStatistics
DependentPredictedStdErrorStdErrorStudentCook's
ObsVariableValueMeanPredictResidualResidualResidual-2-1012D
18.19548.26250.0209-0.06710.0436-1.539|***||0.181
28.28478.31010.0198-0.02540.0441-0.576|*||0.022
38.32468.32570.0175-0.0010350.0451-0.0230|||0.000
48.37358.31410.01710.05940.04521.313||**|0.082
58.43888.39840.01620.04050.04560.888||*|0.033
68.53318.49680.01470.03630.04610.787||*|0.021
78.69578.65710.01280.03870.04660.829||*|0.017
88.83008.85270.0136-0.02270.0464-0.489|||0.007
98.89648.91550.0125-0.01910.0467-0.409|||0.004
108.98518.96410.01110.02100.04710.446|||0.004
119.03439.03010.01040.0042310.04720.0896|||0.000
128.99348.98780.01050.0056180.04720.119|||0.000
139.05549.07110.0302-0.01570.0377-0.416|||0.037
149.17519.17230.02590.0028170.04080.0690|||0.001
159.32199.32550.0186-0.0036550.0446-0.0819|||0.000
169.44729.57400.0120-0.12680.0469-2.706|*****||0.160
179.53159.60530.0123-0.07380.0468-1.579|***||0.057
189.59739.65460.0128-0.05730.0466-1.229|**||0.038
199.66679.69040.0132-0.02370.0465-0.510|*||0.007
209.73159.71940.01350.01210.04640.262|||0.002
219.79049.76060.01400.02980.04630.645||*|0.013
229.85099.80690.01470.04400.04610.956||*|0.031
SAS系统2009年09月28日星期一下午09时41分35秒19
TheREGProcedure
Model:
MODEL1
DependentVariable:
y
OutputStatistics
DependentPredictedStdErrorStdErrorStudentCook's
ObsVariableValueMeanPredictResidualResidualResidual-2-1012D
239.93339.85590.01550.07740.04581.689||***|0.109
2410.01049.96660.01850.04380.04470.981||*|0.055
2510.096010.07530.02270.02080.04270.486|||0.022
SumofResiduals5.15769E-14
SumofSquaredResiduals0.05146
PredictedResidualSS（PRESS）0.06334
R方为0.9135.接近于1，模型拟合得很好。
回
升级会员 