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试验设计与数据处理作业doc
试验设计与数据处理作业
姓名:
班级:
学号:
3-7
SAS分析结果如下:
金球:
及
置信度为0.9的置信区间分别为:
铂球:
及
置信度为0.9的置信区间分别为:
3-13
取假设H0:
u1-u2≤0和假设H1:
u1-u2>0用sas分析结果如下:
SampleStatistics
GroupNMeanStd.Dev.Std.Error
----------------------------------------------------
x80.2318750.01460.0051
y100.20970.00970.0031
HypothesisTest
Nullhypothesis:
Mean1-Mean2=0
Alternative:
Mean1-Mean2^=0
IfVariancesAretstatisticDfPr>t
----------------------------------------------------
Equal3.878160.0013
NotEqual3.70411.670.0032
由此可见p值远小于0.05,可认为拒绝原假设,即认为2个作家所写的小品文中由3个字母组成的词的比例均值差异显著。
3-14
用sas分析如下:
HypothesisTest
Nullhypothesis:
Variance1/Variance2=1
Alternative:
Variance1/Variance2^=1
-DegreesofFreedom-
FNumer.Denom.Pr>F
----------------------------------------------
2.27790.2501
由p值为0.2501>0.05(显著性水平),所以接受原假设,两方差无显著差异
4-1
Sas分析结果如下:
DependentVariable:
y
Sumof
SourceDFSquaresMeanSquareFValuePr>F
Model41480.823000370.20575040.88<.0001
Error15135.8225009.054833
CorrectedTotal191616.645500
R-SquareCoeffVarRootMSEyMean
0.91598513.120233.00912522.93500
SourceDFAnovaSSMeanSquareFValuePr>F
c41480.823000370.20575040.88<.0001
由结果可知,p值小于0.001,故可认为在水平a=0.05下,这些百分比的均值有显著差异。
4-2
SAS分析如下:
TheGLMProcedure
DependentVariable:
R
Sumof
SourceDFSquaresMeanSquareFValuePr>F
Model1182.83333337.53030301.390.2895
Error1265.00000005.4166667
CorrectedTotal23147.8333333
R-SquareCoeffVarRootMSERMean
0.56031622.342782.32737310.41667
SourceDFTypeISSMeanSquareFValuePr>F
m244.3333333322.166666674.090.0442
n311.500000003.833333330.710.5657
m*n627.000000004.500000000.830.5684
SourceDFTypeIIISSMeanSquareFValuePr>F
m244.3333333322.166666674.090.0442
n311.500000003.833333330.710.5657
m*n627.000000004.500000000.830.5684
由结果可知,在不同浓度下得率有显著差异,在不同温度下得率差异不明显,交互作用的效应不显著。
5-3
用L9(34)确定配比试验方案:
试验方案
因素
试验号
A
B
C
D
1
2
3
4
5
6
7
8
9
1(0.1份)
1
1
2(0.3份)
2
2
3(0.2份)
3
3
1(0.3份)
2(0.4份)
3(0.5份)
1
2
3
1
2
3
1(0.2份)
2(0.1份)
3(0.1份)
2
3
1
3
1
2
1(0.5份)
2(0.3份)
3(0.1份)
3
1
2
2
3
1
以1号条件为例,表中四个数值的组成比为:
A:
B:
C:
D=0.1:
0.3:
0.2:
0.5
配比方案中,要求各行四个比值之和为1。
在1号条件中,四种数值分别是
其余实验条件按相同方法可得。
6-5
(1)作出散点图如下:
(2)SAS分析结果如下:
DependentVariable:
y
AnalysisofVariance
SumofMean
SourceDFSquaresSquareFValuePr>F
Model238.9371419.468579.540.0033
Error1224.476192.03968
CorrectedTotal1463.41333
RootMSE1.42817R-Square0.6140
DependentMean30.03333AdjR-Sq0.5497
CoeffVar4.75530
ParameterEstimates
ParameterStandard
VariableDFEstimateErrortValuePr>|t|
Intercept119.033333.277555.81<.0001
t111.008570.356432.830.0152
t21-0.020380.00881-2.310.0393
故回归方程为:
6-6
(1)作线性回归分析结果如下:
由分析结果得回归方程为:
由p值都小于0.1可知,每项都是显著的,方程也是显著的。
(2)
由分析结果可知,在a=0.05下,仅有x3和x1应当引入方程。
故所求方程为:
6-9
分析结果如下:
DependentVariable:
y
StepwiseSelection:
Step1
Variablet9Entered:
R-Square=0.3473andC(p)=175.7517
AnalysisofVariance
SumofMean
SourceDFSquaresSquareFValuePr>F
Model176.2438976.243897.450.0163
Error14143.2837110.23455
CorrectedTotal15219.52760
ParameterStandard
VariableEstimateErrorTypeIISSFValuePr>F
Intercept8.229801.38618360.7494935.25<.0001
t90.010560.0038776.243897.450.0163
Boundsonconditionnumber:
1,1
------------------------------------------------------------------------------------------------------
StepwiseSelection:
Step2
Variablet13Entered:
R-Square=0.6717andC(p)=84.4265
AnalysisofVariance
SumofMean
SourceDFSquaresSquareFValuePr>F
Model2147.4655173.7327613.300.0007
Error1372.062095.54324
CorrectedTotal15219.52760
ParameterStandard
VariableEstimateErrorTypeIISSFValuePr>F
Intercept18.334832.99803207.3226437.40<.0001
t90.011730.0028792.8173316.740.0013
t13-1.899380.5298971.2216212.850.0033
------------------------------------------------------------------------------------------------------
StepwiseSelection:
Step3
Variablet5Entered:
R-Square=0.7627andC(p)=60.2727
AnalysisofVariance
SumofMean
SourceDFSquaresSquareFValuePr>F
Model3167.4249255.8083112.850.0005
Error1252.102684.34189
CorrectedTotal15219.52760
ParameterStandard
VariableEstimateErrorTypeIISSFValuePr>F
Intercept19.499412.70837225.0645251.84<.0001
t50.001630.0007617619.959414.600.0532
t90.007280.0032821.446264.940.0462
t13-2.193050.4885687.4851520.150.0007
Boundsonconditionnumber:
1.8185,13.825
------------------------------------------------------------------------------------------------------
Allvariablesleftinthemodelaresignificantatthe0.1500level.
Noothervariablemetthe0.1500significancelevelforentryintothemodel.
SummaryofStepwiseSelection
VariableVariableNumberPartialModel
StepEnteredRemovedVarsInR-SquareR-SquareC(p)FValuePr>F
1t910.34730.3473175.7527.450.0163
2t1320.32440.671784.426512.850.0033
3t530.09090.762760.27274.600.0532
由结果可知,y=19.49941+0.00163
+0.00728
-2.19305
6-10
(1)散点图如下:
可以采用Logistic拟合此数据。
(2)用Logistic模拟结果为:
DependentVariabley
Method:
Gauss-Newton
Sumof
IterbcaSquares
03.71802.000021.00001124.1
13.64081.849314.8393570.9
23.54751.668414.9977534.7
33.47041.520815.2362499.4
43.40461.396315.4814464.3
53.34691.288715.7348429.2
63.29551.194315.9985394.1
73.24911.110716.2735359.1
83.20691.036016.5601324.4
93.16840.969116.8579290.5
103.13310.909117.1660257.6
113.10080.855117.4829226.3
123.07120.806717.8067196.8
133.04420.763218.1349169.7
143.01950.724218.4653145.1
152.99710.689218.7951123.1
162.97680.658019.1220104.0
172.95840.630019.443887.4241
182.94200.605019.758673.4129
192.92720.582720.064861.7148
202.91400.562820.361052.0895
212.90230.545020.646444.2826
222.89200.529120.920338.0422
232.88280.514921.182233.1304
242.87480.502121.431929.3307
252.86790.490721.669326.4509
262.86180.480421.894624.3243
272.85660.471122.107822.8087
282.85220.462822.309421.7843
292.84840.455322.499521.1514
302.84530.448622.678720.8276
312.84280.442522.847220.7456
WARNING:
Stepsizeshowsnoimprovement.
WARNING:
PROCNLINfailedtoconverge.
EstimationSummary(NotConverged)
MethodGauss-Newton
Iterations31
Subiterations29
AverageSubiterations0.935484
R0.653053
PPC(c)0.012486
TheNLINProcedure
EstimationSummary(NotConverged)
RPC.
Object0.00394
Objective20.74557
ObservationsRead15
ObservationsUsed15
ObservationsMissing0
NOTE:
Aninterceptwasnotspecifiedforthismodel.
SumofMeanApprox
SourceDFSquaresSquareFValuePr>F
Regression33245.51081.8625.77<.0001
Residual1220.74561.7288
UncorrectedTotal153266.3
CorrectedTotal14949.9
Approx
ParameterEstimateStdErrorApproximate95%ConfidenceLimits
b2.84280.004882.83212.8534
c0.44250.003210.43550.4494
a22.84720.574921.594724.0998
ApproximateCorrelationMatrix
bca
b1.00000000.7483922-0.2191675
c0.74839221.0000000-0.4085662
a-0.2191675-0.40856621.0000000
故得
7-1
n=9
作变换
,则x1=1,x2=2,x3=3,…,x9=9。
并可设
=b0+b1Ф1(x)+b2Ф2(x)+b2Ф2(x)+b4Ф4(x)
对于n=9,查附表6,利用SAS软件进行回归多项式分析,结果如下:
根据结果分析b0,b1,b2的P值小于0.05,是显著的,
b3,b4的P值大于0.05是不显著的,所以只需要配要二次项就行了。
当n=9时,有:
将
代入上式得所求多项式回归方程:
7-3
本题属于一次回归的正交设计
采用二水平,做变换:
x1=
,x2=
,x3=
,x4=
试验方案
试验号
x1
x2
x3
x4
y’
1
2
3
4
5
6
7
8
1
1
1
-1
-1
-1
-1
-1
1
1
-1
-1
1
1
-1
-1
1
-1
1
-1
1
-1
1
-1
1
-1
-1
1
-1
1
1
-1
5.4
3.4
0.8
0.3
-2.5
-1
-3.3
-3.6
程序如下:
dataE1;
inputx1-x4y;
cards;
11115.4
11-1-13.4
1-11-10.8
1-1-110.3
-111-1-2.5
-11-11-1
-1-111-3.3
-1-1-1-1-3.6
;
procregdata=E1;
modely=x1-x4;
run;
8-1
安排方案如下:
因素
试验号
Z1
Z2
Z3
1
2.0
600
24
2
3.4
800
22
3
4.8
500
20
4
6.2
700
18
9-1
(1)反射点E的坐标(5,
,0)
(2)(i)扩大,а>1(ii)内收缩,а<0(iii)收缩,0<а<1
(3)新单纯形各点坐标B(2,4,3),A’(1.5,3,3.5),C’(2.5,2.5,2.5),D”(3,3.5,2)
10-4
分析结果如下:
经分析可知,在a=0.05的情况下,一次项均不显著,二次项、交互项均是显著的。
12-1PPT上习题
记
其中优等品10件,一等品30件,二等品40件,20件三等品,所有标准分依次是
,查标准正态表得到标准分依次是:
-1.64,-0.67,0.25;1.28
14-3
SAS分析结果如下:
分成9类:
3,5一类,其他各为一类;
分成8类:
1,3,5一类,其他各为一类;
分成7类:
1,3,5一类,8,10一类,其它各为一类;
分成6类:
1,3,5,6一类,8,10一类,其他各为一类;
分成5类:
1,3,5,6一类,8,9,10一类,其他各为一类;
分成4类:
1,2,3,5,6一类,8,9,10一类,其他各为一类;
分成3类:
1,2,3,5,6,8,9,10一类,4,7各为一类;
分成2类:
1,2,3,4,5,6,8,9,10一类,7为一类。
14PPT补充
15
单指标评价结果归一化处理得:
权向量a=(0.300.250.150.200.10)
a·R=(0.1333,0.4833,0.2223,0.1611)
(1)
根据最大隶属度原则0.48333所对应的评语为一般。
根据秩加权平均原则,用1、2、3、4分别代表差、一般、良好、优
A=1×0.1611+2×0.2223+3×0.4833+4×0.1333=2.588
位于一般与良好之间,且该食品一般偏良
(2)
100×0.1611+80×0.2223+60×0.4833+40×0.1333=68.2245
评分值为:
P=68.2245分