实验设计与数据处理第三四五章例题及课后习题答案

于是 三元线性回归方程为：y=0.197+0.0455x1-0

（1）F检验例4-6

试验号

1

2

3

4

5

6

7

8

SUM

AVE反应温度x1/℃反应时间x2/h反应物含量x3/%得率y701017.67010310.3703018.97030311.2901018.49010311.1903019.89030312.66401601679.9802029.9875

SUMMARY OUTPUT

回归统计

Multiple R0.99645389

R Square0.992920354

Adjusted R 0.987610619

标准误差

观测值方差分析0.1837117318

df回归分析残差

总计347SS18.933750.13519.06875

标准误差

0.554949322

0.006495191

0.006495191

0.064951905MS6.311250.03375F187

CoefficientsIntercept2.1875X Variable 0.04875X Variable 0.06375X Variable 1.3125t Stat3.9418013747.5055534999.81495457620.20725942P-value0.0169340.0016860.0006043.54E-05

所以得到的线性回归方程表达式为：y=2.1875+0.04875x1+0.06375x2+1.3125x3

例4-7

p/atm

M/(mol/min)2.010.7631.780.7151.750.711.730.695

1

2

3

4

5

6

7

8

9

10

SUMp/atm2.011.781.751.731.681.621.41.360.930.5314.79M/(mol/min)0.7630.7150.710.6950.6980.6730.630.6120.4980.3716.365xy2xilg(pi)lg(Mi)0.303196057-0.1174754620.0919280.250420002-0.1456939580.062710.243038049-0.1487416510.0590670.238046103-0.1580151950.0566660.225309282-0.1561445770.0507640.209515015-0.1719849360.0438970.146128036-0.2006594510.0213530.133538908-0.2132485780.017833-0.031517051-0.3027706570.000993-0.27572413-0.430626090.0760241.44195027-2.0453605560.481235

AVE1.479

SUMMARY OUTPUT0.63650.144195027-0.204536056

回归统计

Multiple R0.999492866R Square0.998985989

Adjusted R 0.998859237标准误差0.00319584

观测值10方差分析

df

回归分析

残差

总计189SS0.0804964268.17071E-050.080578133

标准误差

0.001341014

0.006113002F

0.01(1,8)=11.3MSF0.0804964267881.4591.02134E-05CoefficientsIntercept-0.282790341X Variable 0.542697532t StatP-value-210.8779792.86E-1688.777581472.89E-13

例4-8

xi

yi

i

1

2

3

4

5

6

7

8

9

SUM

AVExi1345678910535.888889yi2781011121098778.55555555612x11345678910535.88888888937x248y1297168251036114912641081910083817742.333333338.555556510

回归统计

Multiple R0.981636002

R Square0.96360924

Adjusted R 0.951478987

标准误差0.643254553

观测值9

方差分析

df

回归分析

残差

总计268F0.01(2,6)=10.92SS65.73956372.48265851868.22222222

标准误差

0.846062418

0.330019174

0.028576121MSF32.8697818579.438510.41377642CoefficientsIntercept-1.715966387X Variable 3.750076394X Variable -0.279029794t Stat-2.02817942211.36320764-9.764439272P-value0.0888882.78E-056.63E-05

例4-9

i

1

2

3

4

5

6

7

sumx111.41.82.22.633.415.4x213192510162228133x31.5312.50.523.514y0.330.3360.2940.4760.2090.4510.4822.578

SUMMARY OUTPUT回归统计

Multiple R0.983812569R Square0.967887171

Adjusted R 0.935774341标准误差0.026331591

观测值7方差分析df回归分析残差

总计336SS0.0626933710.0020800580.064773429

标准误差

0.042352824

0.047467569

0.012883654

0.005824205F0.05(3,3)=9.28MSF0.0208977930.14020.000693353CoefficientsIntercept0.057886497X Variable 0.252172538X Variable -0.064840835X Variable 0.028317025t Stat1.366768285.312522719-5.0327985034.861955457P-value0.2651140.0130250.0151190.016617

习题3.1

颜色

橘黄色

粉色

绿色

无色销售额/万元25.130.828.532.426.531.227.930.828.728.325.129.629.127.924.231.7

方差分析：单因素方差分析

SUMMARY

组

行 1

行 2

行 3

行 4观测数5555求和136.6147.8132.2157.3平均27.3229.5626.4431.46方差2.6722.1433.2981.658

方差分析

差异源

组间

组内SS76.845539.084df316MS25.615166672.44275F10.4862

总计115.929519习题3.2乙炔流量/（L/min）

1

1.5

2

2.5空气流量/（L/min）91081.580.381.879.476.175.467.968.7881.181.47560.4118079.175.469.8

方差分析：无重复双因素分析

SUMMARY

行 1

行 2

行 3

行 4

列 1

列 2

列 3

列 4

列 5观测数555544444求和399.9397.6372.7335.5297.9307.3303.8304.3292.4平均79.9879.5274.5467.1方差3.1375.5074.52814.48574.47596.742576.82542.262575.9527.8966776.07521.462573.115.9

方差分析

差异源

行

列

误差

总计SS537.637535.47375.155648.2655df341219MSF179.212528.614868.868251.4159946.262916667

习题3.3

铝材材质去离子水

1

1

2

2自来水2.31.81.51.55.65.35.34.8

3

31.82.37.47.4

方差分析：可重复双因素分析

SUMMARY

1观测数求和平均

方差

2

观测数

求和

平均

方差

3

观测数

求和

平均

方差

总计

观测数

求和

平均

方差24.12.050.125214.87.40418.94.7259.5825231.50210.15.050.125413.13.2754.242524.12.050.125210.95.450.0454153.753.91去离子水自来水总计611.21.8666666670.130666667635.85.9666666671.298666667

方差分析

差异源

样本

列

交互

内部

总计SS4.37166666750.432.3550.4257.57666667df212611MSF2.18583333331.2261950.43720.42861.177516.821430.07

习题4.1

c/%(x)T/℃（y)

19.6105.4

20.5106

22.3

25.1

26.3

27.8

29.1107.2108.9109.6110.7111.5

i

1

2

3

4

5

6

7

总和

平均x19.620.522.325.126.327.829.1170.724.38571y105.4106107.2108.9109.6110.7111.5759.3108.4714286xi2384.16420.25497.29630.01691.69772.84846.814243.05yi211109.161123611491.8411859.2112012.1612254.4912432.2582395.11xiyi2065.8421732390.562733.392882.483077.463244.6518567.38

SUMMARY OUTPUT

回归统计

Multiple R0.999752712

R Square0.999505486

Adjusted R 0.999406583

标准误差0.056916528观测值7

方差分析df

回归分析

残差15SS32.738088260.016197456MSF32.7380882610105.940.003239491

总计632.75428571标准误差0.156270601

0.006347274t StatP-value594.5544392.55E-13100.52828121.85E-09CoefficientsIntercept92.91137938X Variable 0.638080517

习题4.2

T/K

273

283

293

313

333

353c/%202531344658lnTlnc2.4361626471.3010299962.4517864361.3979400092.466867621.4913616942.4955443381.5314789172.5224442341.662757832

2.5477747051.763427994回归统计

SUMMARY OUTPUT

回归统计

Multiple R0.987714594

R Square0.97558012

Adjusted R 0.969475149

标准误差0.029578225

观测值方差分析df回归分析残差总计6145SS0.139805290.0034994850.143304776标准误差

0.764779948

0.307501966

0.000291085

3.88720636MS0.139805290.000874871F159.801CoefficientsIntercept-8.141896159X Variable 3.88720636t StatP-value-10.646063850.00044112.641240680.000225

习题4.3

试验号

1

2

3

4

5

6

7煎煮时间/min(x1)煎煮次数(x2)加水量/倍(x3)含量/(mg/L)y301815402113750374660110267026348039579031257

SUMMARY OUTPUT

回归统计

Multiple R0.992299718

R Square0.984658731

Adjusted R 0.969317462

标准误差2.742554455

观测值7

方差分析

df

回归分析

残差

总计336SS1448.29232822.564814811470.857143

标准误差

5.352918185MSF482.764109364.183667.521604938CoefficientsIntercept-12.61111111t StatP-value-2.3559319750.099767

X Variable 0.175

X Variable 13.71296296

X Variable 1.2870370370.0669114771.5612678040.5371472552.6153958490.0793158.7832227930.0031092.3960599720.096215

习题4.4

试验号T/℃Na2O(x1)/%

11029

21011

31016

41006

5993

61004

7967

8999

9992

10980

11980

12984

13965

141006

15988

16984

17967

18987

19979

20988

21968

22940

23956

24956

25925

SUMMARY OUTPUT

回归统计

Multiple R0.866175908

R Square0.750260704

Adjusted R 0.714583661

标准误差12.79120464siO2(x2)/%CaO(x3)/%729.1728.1727.173.38.873.36.873.38.173.37.173.36.174.37.8747.1746.1747.1716.1719.1727.1729.1728.1727.1728.1726.1738.1737.1736.1738.1736.114141414141414141414141415151515151515151515151515

观测值方差分析df回归分析残差

总计2532124SS10322.086763435.91323713758

标准误差

96.99555718

15.3627836

0.249355095

2.688135002MSF3440.69558821.02923163.6149161CoefficientsIntercept1557.058911X Variable 38.64532374X Variable -1.121266308X Variable 6.484236525t Stat16.052888982.515515725-4.4966649182.412169226P-value2.89E-130.0200930.0001980.02509

所以得到的线性回归方程表达式为：y=1557.06+38.65x1-1.12x1x2+6.48x3

根据偏回归系数的大小，可知三个因素的主次顺序为：x1>x3>x2。

习题5.1

优选过程：

1、

首先在试验范围0.618处做第一个实验，这一点的温度为：x1=340+(420-340)×0.6

2、在这点的对称点，即0.382处做一个实验，这一点的温度为：x1=420-(420-340)×0

3、比较两次的实验结果，发现第一点比第二点的合成率高，故舍去370.56以下部分，

4、比较两次的实验结果，发现第一点比第三点的合成率高，故舍去389.44608以下部分

5、比较两次的实验结果，发现第一点比第四点的合成率高，故舍去401.11767744以上

习题5.3

电解质温度

电解率6594.3

7498.98081.5

目标函数

101.4993x=70.62664887

则下一个实验点为70.63℃。

习题5.4.

黄金分割法

首先在实验范围的0.618处做第一个实验，这一点的碱液用量为

x1=20+(80-20)*0.618=57.08(ml)

在这一点的对称点，即0.382处做第二个实验，这一点的碱液用量为

x2=80-(80-20)*0.618=42.92(ml)

比较两次试验结果，第二点较第一点好，则去掉57.08以上的部分，然后在20ml与57.08ml之间，找x2的

x3=57.08-(57.08-20)*0.618=34.165(ml)

比较第二点与第三点，第二点较好，则去掉34.165以下的部分，然后在34.165ml与57.08ml之间，找x2的

x4=34.165+(57.08-34.165)*0.618=48.326(ml)

比较第二点与第四点，第四点较好，则去掉42.29以下的部分，然后在42.29ml与57.08ml之间，找x4的对

x5=42.29+(57.08-42.29)*0.618=51.43(ml)

由于x5属于50ml到55ml之间，则为最佳点。

习题5.5

对开法

在直角坐标系中画出一矩形代表优选范围：20<x<100,30<y<160.

在中线x=(20+100)/2=60上用单因素法找到最大值，设最大值在P点。

再在中线y=(30+160)/2=90上用单因素法找到最大值，设最大值在Q点。

比较P和Q的结果，如果Q大，去掉x<60部分，否则去掉另一半。再用同样的方法来处理余下的半个矩形

不断地去其一半，逐步得到所需要的结果。

习题5.2

解：由于实验范围在3到8桶之间，中间正好有5格，则第一次实验点在3/5处，即6桶

第二次实验点在3/5的对称点2/5处，即5桶处。比较两个实验点的结果，第一点处较好，

则去掉5桶以下的部分，实验范围在5到8桶之间，中间正好有3格，第三次试验点选在2/3处，

即7桶处。比较第一点与第三点的结果，第一点较好。则最佳点是第一点，即6桶。

回归方程为：y=0.197+0.0455x1-0.00377x2+0.0715x3

y2

57.76

106.09

79.21

125.44

70.56

123.21

96.04

158.76

817.07x124900490049004900810081008100810052000x221001009009001001009009004000x321919191940x1x2700700210021009009002700270012800x1x3702107021090270902701280x2x31030309010303090320

Significance F

9.37555E-05Lower 95%Upper 95%下限 95.0%上限 95.0%

0.6467136713.7282860.6467143.728286

0.030716460.0667840.0307160.066784

0.045716460.0817840.0457160.081784

1.1321646011.4928351.1321651.492835

1.681.621.41.36

0.6980.6730.630.612

y2

ixiyi

0.013800484-0.03562

0.021226729-0.03648

0.022124079-0.03615

0.024968802-0.03761

0.024381129-0.03518

0.029578818-0.03603

0.040264215-0.02932

0.045474956-0.02848

0.0916700710.009542

0.185438830.118734

0.498928113-0.14660.930.530.4980.371.06375x2+1.3125x3

Significance F

2.89205E-13Lower 95%Upper 95%下限 95.0%上限 95.0%

-0.285882725-0.2797-0.28588-0.2797

0.5286009250.5567940.5286010.556794

6789

1112109

y2x12x22x1x2x1y

4111

4998127

641625664

10025625125

121361296216

144492401343

100644096512

81816561729

64100100001000

727381253173017108x2y2213250668480818049626312825039658864072980035960.01(1,8)=11.3

0.01(2,6)=10.92Significance F

4.81918E-05Lower 95%Upper 95%下限 95.0%上限 95.0%

-3.7862065410.354274-3.786210.354274

2.9425485694.5576042.9425494.557604

-0.348953042-0.20911-0.34895-0.20911

X1=x3

1.5

3

1

2.5

0.5

2

3.5

14X2=x32X3=x1x3y2X12X22X322.251.50.10892.255.06252.2594.20.11289698117.6411.80.086436113.246.255.50.2265766.2539.062530.250.251.30.0436810.250.06251.69460.2034014163612.2511.90.23232412.25150.0625141.613532.21.01421435292.25232.68

3,3)=9.28

Significance F0.00967471Lower 95%Upper 95%下限 95.0%上限 95.0%

-0.0768990930.192672-0.07690.192672

0.1011095490.4032360.101110.403236

-0.105842372-0.02384-0.10584-0.02384

0.0097818060.0468520.0097820.046852

27.2

29.6

26.5

32.8

P-valueF crit

0.000466143.238872

12

77

75.9

70.8

68.7P-valueF crit9.44035E-063.490295

0.2874223173.259167

P-value

0.0006734231.76634E-07

0.00346704F crit5.1432535.9873785.143253

Significance F1.84673E-09

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