实验设计与数据处理第三四五章例题及课后习题答案

1、例4-5试验号x1x2x3yy211131.50.330.108921.41930.3360.11289631.82510.2940.08643642.2102.50.4760.22657652.6160.50.2090.043681632220.4510.20340173.4283.50.4820.232324总和15.4133142.5781.014214平均2.2192 0.368286l114.48方程目标函数l2225211e-061e-06l33721e-06l1216.83 2.32e-09l2310.54 7.24e-11l311.4l1y0.2404于是 三元线性回归方程为：

2、y=0.197+0.0455x1-0.00377x2+0.0715x3l2y0.564l3y0.5245检验线性回归方程的显著性方差分析表（1）f检验sst0.064773429差异源ssr0.046300406回归sse0.018473023残差总和例4-6试验号反应温度x1/反应时间x2/h反应物含量x3/% 得率yy21701017.657.7627010310.3106.093703018.979.2147030311.2125.445901018.470.5669010311.1123.217903019.896.0489030312.6158.76sum6401601679.981

3、7.07ave802029.9875summary output回归统计multiple r0.99645389r square0.992920354adjusted r square0.987610619标准误差0.183711731观测值8方差分析dfssmsfsignificance f回归分析318.933756.311251879.37555e-05残差40.1350.03375总计719.06875coefficients标准误差t statp-valuelower 95%intercept2.18750.5549493223.941801374 0.0169340.6467136

4、71x variable 10.048750.0064951917.505553499 0.0016860.03071646x variable 20.063750.0064951919.814954576 0.0006040.04571646x variable 31.31250.06495190520.20725942 3.54e-051.132164601所以得到的线性回归方程表达式为：y=2.1875+0.04875x1+0.06375x2+1.3125x3l11800l22800l338p10.315761009p20.412918242p30.850125793t17.505553

5、499t29.814954576t320.20725942例4-7p/atm2.011.781.751.731.68m/(mol/min)0.7630.7150.710.6950.698p/atmm/(mol/min)xyxi2yi2lg(pi)lg(mi)12.010.7630.303196057-0.117475462 0.0919280.01380048421.780.7150.250420002-0.1456939580.062710.02122672931.750.710.243038049-0.148741651 0.0590670.02212407941.730.6950.238

6、046103-0.158015195 0.0566660.02496880251.680.6980.225309282-0.156144577 0.0507640.02438112961.620.6730.209515015-0.171984936 0.0438970.02957881871.40.630.146128036-0.200659451 0.0213530.04026421581.360.6120.133538908-0.213248578 0.0178330.04547495690.930.498-0.031517051-0.302770657 0.0009930.0916700

7、71100.530.371-0.27572413-0.43062609 0.0760240.18543883sum14.796.3651.44195027-2.045360556 0.4812350.498928113ave1.4790.63650.144195027-0.204536056summary output回归统计multiple r0.999492866r square0.998985989adjusted r square0.998859237标准误差0.00319584观测值10方差分析f0.01(1,8)=11.3dfssmsfsignificance f回归分析10.08

8、04964260.080496426 7881.4592.89205e-13残差88.17071e-051.02134e-05总计90.080578133coefficients标准误差t statp-valuelower 95%intercept-0.2827903410.001341014-210.877979 2.86e-16-0.285882725x variable 1 0.5426975320.00611300288.77758147 2.89e-130.528600925例4-8xi13456yi2781011ixiyix1x2yy211211242373974934841686

9、4451052510100561163611121671274912144781086410100899981981910810100864sum53775338177727ave5.8888898.5555555565.88888888942.33333333 8.55555612108642002468101214xyseries1summary output回归统计multiple r0.981636002r square0.96360924adjusted r square0.951478987标准误差0.643254553观测值9方差分析f0.01(2,6)=10.92dfssmsf

10、significance f回归分析265.739563732.86978185 79.438514.81918e-05残差62.4826585180.41377642总计868.22222222coefficients标准误差t statp-valuelower 95%intercept-1.7159663870.846062418-2.028179422 0.088888-3.786206541x variable 1 3.7500763940.33001917411.36320764 2.78e-052.942548569x variable 2 -0.2790297940.028576

11、121-9.764439272 6.63e-05-0.348953042例4-9ix1x2x3yx1=x311131.50.331.521.41930.336331.82510.294142.2102.50.4762.552.6160.50.2090.5632220.451273.4283.50.4823.5sum15.4133142.57814summary output回归统计multiple r0.98381256912108642002468101214xyseries1r square0.967887171adjusted r square0.935774341标准误差0.02633

12、1591观测值7方差分析f0.05(3,3)=9.28dfssmsfsignificance f回归分析30.0626933710.0208977930.14020.00967471残差30.0020800580.000693353总计60.064773429coefficients标准误差t statp-valuelower 95%intercept0.0578864970.0423528241.36676828 0.265114-0.076899093x variable 1 0.2521725380.0474675695.312522719 0.0130250.101109549x va

13、riable 2 -0.0648408350.012883654-5.032798503 0.015119-0.105842372x variable 3 0.0283170250.0058242054.861955457 0.0166170.009781806习题3.1颜色销售额/万元橘黄色26.528.725.129.127.2粉色31.228.330.827.929.6绿色27.925.128.524.226.5无色30.829.632.431.732.8方差分析：单因素方差分析summary组观测数求和平均方差行 15136.627.322.672行 25147.829.562.143

14、行 35132.226.443.298行 45157.331.461.658方差分析差异源ssdfmsfp-value组间76.8455325.6151666710.48620.00046614组内39.084162.44275总计115.929519习题3.2乙炔流量空气流量/（l/min）/（l/min）89101112181.181.580.380771.581.481.879.479.175.927576.175.475.470.82.560.467.968.769.868.7方差分析：无重复双因素分析summary观测数求和平均方差行 15399.979.983.137行 25397

15、.679.525.507行 35372.774.544.528行 45335.567.114.485列 14297.974.47596.7425列 24307.376.82542.2625列 34303.875.95 27.89667列 44304.376.07521.4625列 54292.473.115.9方差分析差异源ssdfmsfp-value行537.63753179.2125 28.614869.44035e-06列35.47348.86825 1.4159940.287422317误差75.155126.262916667总计648.265519习题3.3铝材材质 去离子水自来水

16、12.35.611.85.321.55.321.54.831.87.432.37.4方差分析：可重复双因素分析summary去离子水自来水总计1观测数224求和4.110.915平均2.055.453.75方差0.1250.0453.912观测数224求和310.113.1平均1.55.053.275方差00.1254.24253观测数224求和4.114.818.9平均2.057.44.725方差0.12509.5825总计观测数66求和11.235.8平均1.8666666675.966666667方差0.1306666671.298666667方差分析差异源ssdfmsfp-value样

17、本4.37166666722.185833333 31.226190.000673423列50.43150.43 720.42861.76634e-07交互2.35521.1775 16.821430.00346704内部0.4260.07总计57.5766666711习题4.1c/%(x)t/（y)19.6105.420.510622.3107.225.1108.926.3109.627.8110.729.1111.5浓度与沸点温度之间的关系32272217102104106108110112c/%t/series1ixyxi2yi2xiyi119.6105.4384.1611109.162

18、065.84220.5106420.25112362173322.3107.2497.2911491.842390.56425.1108.9630.0111859.212733.39526.3109.6691.6912012.162882.48627.8110.7772.8412254.493077.46729.1111.5846.8112432.253244.65总和170.7759.34243.0582395.11 18567.38平均24.38571108.4714286summary output回归统计multiple r0.999752712r square0.999505486a

19、djusted r square0.999406583标准误差0.056916528观测值7方差分析dfssmsfsignificance f回归分析132.7380882632.73808826 10105.941.84673e-09残差50.0161974560.003239491总计632.75428571coefficients标准误差t statp-valuelower 95%intercept92.911379380.156270601594.554439 2.55e-1392.50967302x variable 1 0.6380805170.006347274100.52828

20、12 1.85e-090.621764331浓度与沸点温度之间的关系32272217102104106108110112c/%t/series1习题4.2t/kc/%lntlnc273202.4361626471.301029996summary output283252.4517864361.397940009293312.466867621.491361694回归统计313342.4955443381.531478917multiple r333462.5224442341.662757832r square353582.5477747051.763427994adjusted r squ

21、are标准误差观测值方差分析回归分析残差总计interceptx variable 1summary output回归统计multiple r0.987714594r square0.97558012adjusted r square0.969475149标准误差0.029578225观测值6方差分析dfssmsfsignificance f回归分析10.1398052908010.00022547残差40.0034994850.000874871总计50.143304776coefficients标准误差t statp-valuelower 95%某物质的溶解度与绝

22、对温度之间的关系100010010100t/kc/series1intercept-8.1418961590.764779948-10.64606385 0.000441-10.2652657x variable 1 3.887206360.30750196612.64124068 0.0002253.0334440320.0002910853.88720636习题4.3试验号煎煮时间/min(x1) 煎煮次数(x2)加水量/倍(x3)含量/(mg/l)y1301815240211373503746460110265702634680395779031257summary output回归统计

23、multiple r0.992299718r square0.984658731adjusted r square0.969317462标准误差2.742554455观测值7方差分析dfssmsfsignificance f回归分析31448.292328482.7641093 64.183660.003210937残差322.564814817.521604938总计61470.857143coefficients标准误差t statp-valuelower 95%intercept-12.611111115.352918185-2.355931975 0.099767-29.6464858

24、1x variable 10.1750.0669114772.615395849 0.079315-0.037942184x variable 2 13.712962961.5612678048.783222793 0.0031098.744312009x variable 3 1.2870370370.5371472552.396059972 0.096215-0.42240526习题4.4试验号t/na2o(x1)/%sio2(x2)/%cao(x3)/%x1=x11102914729.1142101114728.1143101614727.114410061473.38.81459931

25、473.36.814610041473.38.11479671473.37.11489991473.36.11499921474.37.8141098014747.1141198014746.1141298414747.1141396515716.11514100615719.1151598815727.1151698415729.1151796715728.1151898715727.1151997915728.1152098815726.1152196815738.1152294015737.1152395615736.1152495615738.1152592515736.115summ

26、ary output回归统计multiple r0.866175908r square0.750260704adjusted r square0.714583661标准误差12.79120464观测值25方差分析dfssmsfsignificance f回归分析310322.086763440.695588 21.029231.56843e-06残差213435.913237163.6149161总计2413758coefficients标准误差t statp-valuelower 95%intercept1557.05891196.9955571816.05288898 2.89e-1313

27、55.345608x variable 1 38.6453237415.36278362.515515725 0.0200936.696666383x variable 2 -1.1212663080.249355095-4.496664918 0.000198-1.639828614x variable 3 6.4842365252.6881350022.4121692260.025090.89395378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：x1x3x2。习题5.1优选过程：1、首先

28、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)0.618=389.44.2、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)0.618=370.56.3、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，在370.56-420之间，找x1的对称：x3=420-(420-370.56)0.618=389.44608.4、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，在389.44608-420之间，找x1的对称：x4=420-(420-389.4460

29、8)0.618=401.11767744.5、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以上部分，在389.44608-401.11767744之间，找x1的对称：x5=401.11767744-(401.11767744-389.44608)0.618=393.787.习题5.3电解质温度657480电解率94.398.981.5目标函数101.4993 x=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908070605040302010002040608010012

30、0y = -0.2274x2 + 32.1207x - 1032.7519电解质温度电解率)()()()()()(212131323212221321232232214xxyxxyxxyxxyxxyxxyx-+-+-+-+-=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的对称点x3=57.08-(57.08-20)*0.618=34.165(ml)比较第二

31、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的对称点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的对称点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 x100,30y160.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

32、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x60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桶处，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。x12x22x32x1x2x2x3x1x3x1yx2y

33、x3y11692.251319.51.50.334.290.4951.96361926.6574.20.47046.3841.0083.24625145251.80.52927.350.2944.841006.2522255.51.04724.761.196.762560.2541.681.30.54343.3440.104594844664461.3539.9220.90211.5678412.2595.29811.91.638813.4961.68738.36277935309.4276.532.25.91249.5465.6805方程解a=0.196943b1=0.045463b2=-0

34、.00377b3=0.071493ssdfmsff0.05(3,3)显著性0.0463 m=30.0154332.506389.80.018473 n-m-1=30.0061580.064773 n-1=6x12x22x32x1x2x1x3x2x3x1yx2yx3y490010017007010532767.6490010097002103072110330.949009001210070306232678.94900900921002109078433633.6810010019009010756848.4810010099002703099911133.381009001270090308

35、822949.881009009270027090113437837.85200040004012800128032064311649170.3于是 三元线性回归方程为：y=0.197+0.0455x1-0.00377x2+0.0715x3方差分析表upper 95% 下限 95.0% 上限 95.0%3.728286 0.646714 3.7282860.066784 0.030716 0.0667840.081784 0.045716 0.0817841.492835 1.132165 1.4928351.621.41.360.930.530.6730.630.6120.4980.371x

36、iyi-0.03562-0.03648-0.03615-0.03761-0.03518-0.03603-0.02932-0.028480.0095420.118734-0.1466upper 95% 下限 95.0% 上限 95.0%-0.2797 -0.28588-0.27970.556794 0.528601 0.55679478910121098x12x22x1x2x1yx2y11122981272163162566432128256251255025036129621666396492401343845886440965128064081656172981729100100001000

37、808003812531730174963596upper 95% 下限 95.0% 上限 95.0%0.354274 -3.78621 0.3542744.557604 2.942549 4.557604-0.20911 -0.34895 -0.20911x2=x32x3=x1x3y2x12x22x32x1x2x1x3x2x32.251.50.10892.255.06252.253.3752.253.37594.2 0.11289698117.642712.637.811.8 0.086436113.2411.81.86.255.5 0.2265766.2539.062530.2515.62

38、513.7534.3750.251.3 0.0436810.250.06251.690.1250.650.32546 0.203401416368122412.2511.9 0.23232412.25150.0625141.6142.87541.65145.7753532.2 1.01421435292.25232.689884.7247.45upper 95% 下限 95.0% 上限 95.0%0.192672-0.0769 0.1926720.4032360.10111 0.403236-0.02384 -0.10584 -0.023840.046852 0.009782 0.046852

39、f crit3.238872f crit3.4902953.259167f crit5.1432535.9873785.143253upper 95% 下限 95.0% 上限 95.0%93.31309 92.50967 93.313090.654397 0.621764 0.6543970.9877150.975580.9694750.0295786dfssmsfsignificance f1 0.139805 0.139805159.8010.000225474 0.003499 0.0008755 0.143305coefficients 标准误差t statp-valuelower 9

40、5% upper 95% 下限 95.0% 上限 95.0%-8.14190.76478 -10.6461 0.000441 -10.2652657 -6.01853 -10.2653 -6.018533.887206 0.307502 12.64124 0.000225 3.033444032 4.740969 3.033444 4.740969upper 95% 下限 95.0% 上限 95.0%回归统计-6.01853 -10.2653 -6.018534.740969 3.033444 4.740969upper 95% 下限 95.0% 上限 95.0%4.424264 -29.6465 4.4242640.387942 -0.03794 0.38794218.68161 8.744312 18.681612.996479 -0.42241 2.996479x2=x1x2x3=x3y=