实验设计与数据处理第三四五章例题及课后习题答案.xls

例4-5试验号x1x2x3yy2 11131.50.330.1089 21.41930.3360.112896 31.82510.2940.086436 42.2102.50.4760.226576 52.6160.50.2090.043681 632220.4510.203401 73.4283.50.4820.232324 总和15.4133142.5781.014214 平均2.2192 0.368286 L114.48方程目标函数 L2225211E-061E-06 L33721E-06 L1216.83 2.32E-09 L2310.54 7.24E-11 L311.4 L1y0.2404于是 三元线性回归方程为：y=0.197+0.0455x1-0.00377x2+0.0715x3 L2y0.564 L3y0.5245 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yy2 1701017.657.76 27010310.3106.09 3703018.979.21 47030311.2125.44 5901018.470.56 69010311.1123.21 7903019.896.04 89030312.6158.76 SUM6401601679.9817.07 AVE802029.9875 SUMMARY OUTPUT 回归统计 Multiple R0.99645389 R Square0.992920354 Adjusted 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719.06875 Coefficients标准误差t StatP-valueLower 95% Intercept2.18750.5549493223.941801374 0.0169340.646713671 X Variable 10.048750.0064951917.505553499 0.0016860.03071646 X Variable 20.063750.0064951919.814954576 0.0006040.04571646 X 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+1.3125x3 L11800 L22800 L338 P10.315761009 P20.412918242 P30.850125793 t17.505553499 t29.814954576 t320.20725942 例4-7 p/atm2.011.781.751.731.68 M/(mol/min)0.7630.7150.710.6950.698 p/atmM/(mol/min) xy xi2yi2lg(pi)lg(Mi) 12.010.7630.303196057-0.117475462 0.0919280.013800484 21.780.7150.250420002-0.1456939580.062710.021226729 31.750.710.243038049-0.148741651 0.0590670.022124079 41.730.6950.238046103-0.158015195 0.0566660.024968802 51.680.6980.225309282-0.156144577 0.0507640.024381129 61.620.6730.209515015-0.171984936 0.0438970.029578818 71.40.630.146128036-0.200659451 0.0213530.040264215 81.360.6120.133538908-0.213248578 0.0178330.045474956 90.930.498-0.031517051-0.302770657 0.0009930.091670071 100.530.371-0.27572413-0.43062609 0.0760240.18543883 SUM14.796.3651.44195027-2.045360556 0.4812350.498928113 AVE1.4790.63650.144195027-0.204536056 SUMMARY OUTPUT 回归统计 Multiple R0.999492866 R Square0.998985989 Adjusted R Square0.998859237 标准误差0.00319584 观测值10 方差分析F0.01(1,8)=11.3 dfSSMSFSignificance F 回归分析10.0804964260.080496426 7881.4592.89205E-13 残差88.17071E-051.02134E-05 总计90.080578133 Coefficients标准误差t StatP-valueLower 95% Intercept-0.2827903410.001341014-210.877979 2.86E-16-0.285882725 X Variable 1 0.5426975320.00611300288.77758147 2.89E-130.528600925 例4-8 xi13456 yi2781011 ixiyix1x2yy2 1121124 23739749 348416864 451052510100 561163611121 671274912144 781086410100 899981981 910810100864 SUM53775338177727 AVE5.8888898.5555555565.88888888942.33333333 8.555556 121086420 0 2 4 6 8 10 12 14 x y Series 1 SUMMARY OUTPUT 回归统计 Multiple R0.981636002 R Square0.96360924 Adjusted R Square0.951478987 标准误差0.643254553 观测值9 方差分析F0.01(2,6)=10.92 dfSSMSFSignificance F 回归分析265.739563732.86978185 79.438514.81918E-05 残差62.4826585180.41377642 总计868.22222222 Coefficients标准误差t StatP-valueLower 95% Intercept-1.7159663870.846062418-2.028179422 0.088888-3.786206541 X Variable 1 3.7500763940.33001917411.36320764 2.78E-052.942548569 X Variable 2 -0.2790297940.028576121-9.764439272 6.63E-05-0.348953042 例4-9 ix1x2x3yX1=x3 11131.50.331.5 21.41930.3363 31.82510.2941 42.2102.50.4762.5 52.6160.50.2090.5 632220.4512 73.4283.50.4823.5 sum15.4133142.57814 SUMMARY OUTPUT 回归统计 Multiple R0.983812569 121086420 0 2 4 6 8 10 12 14 x y Series 1 R Square0.967887171 Adjusted R Square0.935774341 标准误差0.026331591 观测值7 方差分析F0.05(3,3)=9.28 dfSSMSFSignificance F 回归分析30.0626933710.0208977930.14020.00967471 残差30.0020800580.000693353 总计60.064773429 Coefficients标准误差t StatP-valueLower 95% Intercept0.0578864970.0423528241.36676828 0.265114-0.076899093 X Variable 1 0.2521725380.0474675695.312522719 0.0130250.101109549 X Variable 2 -0.0648408350.012883654-5.032798503 0.015119-0.105842372 X 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 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）89101112 181.181.580.38077 1.581.481.879.479.175.9 27576.175.475.470.8 2.560.467.968.769.868.7 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 25397.679.525.507 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 12.35.6 11.85.3 21.55.3 21.54.8 31.87.4 32.37.4 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0.1250.0453.91 2 观测数224 求和310.113.1 平均1.55.053.275 方差00.1254.2425 3 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4.1 c/%(x)T/（y) 19.6105.4 20.5106 22.3107.2 25.1108.9 26.3109.6 27.8110.7 29.1111.5 浓度与沸点温度之间的关系 32272217 102 104 106 108 110 112 c/% T/ Series 1 ixyxi2yi2xiyi 119.6105.4384.1611109.162065.84 220.5106420.25112362173 322.3107.2497.2911491.842390.56 425.1108.9630.0111859.212733.39 526.3109.6691.6912012.162882.48 627.8110.7772.8412254.493077.46 729.1111.5846.8112432.253244.65 总和170.7759.34243.0582395.11 18567.38 平均24.38571108.4714286 SUMMARY OUTPUT 回归统计 Multiple R0.999752712 R Square0.999505486 Adjusted 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632.75428571 Coefficients标准误差t StatP-valueLower 95% Intercept92.911379380.156270601594.554439 2.55E-1392.50967302 X Variable 1 0.6380805170.006347274100.5282812 1.85E-090.621764331 浓度与沸点温度之间的关系 32272217 102 104 106 108 110 112 c/% T/ Series 1 习题4.2 T/Kc/%lnTlnc 273202.4361626471.301029996SUMMARY OUTPUT 283252.4517864361.397940009 293312.466867621.491361694回归统计 313342.4955443381.531478917Multiple R 333462.5224442341.662757832R Square 353582.5477747051.763427994Adjusted R Square 标准误差 观测值 方差分析 回归分析 残差 总计 Intercept X Variable 1 SUMMARY OUTPUT 回归统计 Multiple R0.987714594 R Square0.97558012 Adjusted 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50.143304776 Coefficients标准误差t StatP-valueLower 95% 某物质的溶解度与绝对温度之间的关系 1000100 10 100 T/K c/ Series 1 Intercept-8.1418961590.764779948-10.64606385 0.000441-10.2652657 X Variable 1 3.887206360.30750196612.64124068 0.0002253.033444032 0.000291085 3.88720636 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)y 1301815 24021137 3503746 46011026 5702634 6803957 79031257 SUMMARY OUTPUT 回归统计 Multiple R0.992299718 R Square0.984658731 Adjusted 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61470.857143 Coefficients标准误差t StatP-valueLower 95% Intercept-12.611111115.352918185-2.355931975 0.099767-29.64648581 X Variable 10.1750.0669114772.615395849 0.079315-0.037942184 X Variable 2 13.712962961.5612678048.783222793 0.0031098.744312009 X 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=x1 1102914729.114 2101114728.114 3101614727.114 410061473.38.814 59931473.36.814 610041473.38.114 79671473.37.114 89991473.36.114 99921474.37.814 1098014747.114 1198014746.114 1298414747.114 1396515716.115115 1598815727.115 1698415729.115 1796715728.115 1898715727.115 1997915728.115 2098815726.115 2196815738.115 2294015737.115 2395615736.115 2495615738.115 2592515736.115 SUMMARY OUTPUT 回归统计 Multiple R0.866175908 R Square0.750260704 Adjusted 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2413758 Coefficients标准误差t StatP-valueLower 95% Intercept1557.05891196.9955571816.05288898 2.89E-131355.345608 X Variable 1 38.6453237415.36278362.515515725 0.0200936.696666383 X Variable 2 -1.1212663080.249355095-4.496664918 0.000198-1.639828614 X 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-(420-389.44608)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 9080706050403020100 0 20 40 60 80 100 120 y = -0.2274x2 + 32.1207x - 1032.7519 电解质温度 电解率 )()()( )()()( 2 1 213132321 2 2 2 13 2 1 2 32 2 3 2 21 4 xxyxxyxxy xxyxxyxxy x -+-+- -+-+- = 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：20x100,30y160. 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。 x12x22x32x1x2x2x3x1x3x1yx2yx3y 11692.251319.51.50.334.290.495 1.96361926.6574.20.47046.3841.008 3.24625145251.80.52927.350.294 4.841006.2522255.51.04724.761.19 6.762560.2541.681.30.54343.3440.1045 94844664461.3539.9220.902 11.5678412.2595.29811.91.638813.4961.687 38.36277935309.4276.532.25.91249.5465.6805 方程解 a=0.196943 b1=0.045463 b2=-0.00377 b3=0.071493 SSdfMSFF0.05(3,3)显著性 0.0463 m=30.0154332.506389.8 0.018473 n-m-1=30.006158 0.064773 n-1=6 x12x22x32x1x2x1x3x2x3x1yx2yx3y 490010017007010532767.6 490010097002103072110330.9 49009001210070306232678.9 4900900921002109078433633.6 810010019009010756848.4 810010099002703099911133.3 81009001270090308822949.8 81009009270027090113437837.8 5200040004012800128032064311649170.3 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 3.728286 0.066784 0.030716 0.066784 0.081784 0.045716 0.081784 1.492835 1.132165 1.492835 1.621.41.360.930.53 0.6730.630.6120.4980.371 xiyi -0.03562 -0.03648 -0.03615 -0.03761 -0.03518 -0.03603 -0.02932 -0.02848 0.009542 0.118734 -0.1466 Upper 95% 下限 95.0% 上限 95.0% -0.2797 -0.28588-0.2797 0.556794 0.528601 0.556794 78910 121098 x12x22x1x2x1yx2y 11122 981272163 162566432128 2562512550250 36129621666396 49240134384588 64409651280640 81656172981729 10010000100080800 3812531730174963596 Upper 95% 下限 95.0% 上限 95.0% 0.354274 -3.78621 0.354274 4.557604 2.942549 4.557604 -0.20911 -0.34895 -0.20911 X2=x32X3=x1x3y2X12X22X32X1X2X1X3X2X3 2.251.50.10892.255.06252.253.3752.253.375 94.2 0.11289698117.642712.637.8 11.8 0.086436113.2411.81.8 6.255.5 0.2265766.2539.062530.2515.62513.7534.375 0.251.3 0.0436810.250.06251.690.1250.650.325 46 0.2034014163681224 12.2511.9 0.23232412.25150.0625141.6142.87541.65145.775 3532.2 1.01421435292.25232.689884.7247.45 Upper 95% 下限 95.0% 上限 95.0% 0.192672-0.0769 0.192672 0.4032360.10111 0.403236 -0.02384 -0.10584 -0.02384 0.046852 0.009782 0.046852 F crit 3.238872 F crit 3.490295 3.259167 F crit 5.143253 5.987378 5.143253 Upper 95% 下限 95.0% 上限 95.0% 93.31309 92.50967 93.31309 0.654397 0.621764 0.654397 0.987715 0.97558 0.969475 0.029578 6 dfSSMSFSignificance F 1 0.139805 0.139805159.8010.00022547 4 0.003499 0.000875 5 0.143305 Coefficients 标准误差t StatP-valueLower 95% Upper 95% 下限 95.0% 上限 95.0% -8.14190.76478 -10.6461 0.000441 -10.2652657 -6.01853 -10.2653 -6.01853 3.887206 0.307502 12.64124 0.000225 3.033444032 4.740969 3.033444 4.740969 Upper 95% 下限 95.0% 上限 95.0% 回归统计 -6.01853 -10.2653 -6.01853 4.740969 3.033444 4.740969 Upper 95% 下限 95.0% 上限 95.0% 4.424264 -29.6465 4.424264 0.387942 -0.03794 0.387942 18.68161 8.744312 18.68161 2.996479 -0.42241 2.996