试验设计与数据处理(第二版)课后习题答案

1、试试验验设设计计与与数数据据处处理理课课后后习习题题答答案案第二章习题答案2.10.04150.03550.03360.03120.03020.02890.02770.0271Re17500255002970037600424005090061800693002.2x1234 Mx=1/x=20mmy88.28.38 My=1/y=5mm关系曲线0.10.01100001000000Rex与y的关系图4.543.532.521.510.507.87.988.18.28.38.4xySeries12.3发酵时间/d0123456PH值 5.45.865.95.85.75.6残糖量/（g/l）24

2、.513.311.210.19.58.17.82.4树脂型号 DA-201NKA-9AB-8D-4006D-101S-8NKA-吸附量/(mg/g) 17.1417.771.8713.710.5513.333.67发酵时间与PH值及残糖量的关系图98765432100510152025304.95.15.35.55.75.96.1发酵时间/dph值残糖量PH值DA-201 NKA-9AB-8D-4006 D-101S-8NKA-02468101214161820树脂型号吸附量/(mg/g)x与y的关系图4.543.532.521.510.507.87.988.18.28.38.4xySerie

3、s12.5植物油凝固点/甲乙花生油2.93.5棉子油-6.3-6.2蓖麻油-0.10.5菜籽油5.352.6应用领域 橡胶工业 合成表面活性剂润滑油(脂) 肥皂及洗涤剂金属皂其他比例/%181152321222.9-6.3-0.15.33.5-6.20.55两个产地几种植物油的凝固点数据图花生油棉子油蓖麻油菜籽油-7-6-5-4-3-2-10123456植物油凝固点/甲例/%橡胶工业合成表面活性剂润滑油(脂)肥皂及洗涤剂金属皂其他3.1第三章习题答案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

4、.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-valueF crit组间76.84553 25.6151710.4862 0.000466 3.238872组内39.084162.44275总计115.9295193.2乙炔流量空气流量/（L/min）/（L/min）89101112181.181.580.380771.5

5、81.481.879.479.175.927576.175.475.470.82.560.467.968.769.868.7方差分析：无重复双因素分例/%橡胶工业合成表面活性剂润滑油(脂)肥皂及洗涤剂金属皂其他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

6、 54292.473.115.9方差分析差异源SSdfMSFP-valueF crit行537.63753 179.2125 28.61486 9.44E-06 3.490295列35.47348.86825 1.415994 0.287422 3.259167误差75.15512 6.262917总计648.2655193.3铝材材质 去离子水自来水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

7、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1.866666667 5.966667方差0.130666667 1.298667方差分析差异源SSdfMSFP-valueF crit样本4.3716666672 2.185833 31.22619 0.000673 5.143253列50.43150.43 720.4286 1.77E-07 5.987378交互2.35521.1775 16.82143 0.003467

8、5.143253内部0.4260.07总计57.57666667114.1c/%(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/Series1ixyxi2yi2xiyi119.6105.4384.16 11109.162065.84220.5106420.25112362173322.3107.2497.29 11491.842390.56425.1108.9630.01 11859.212733.39526.3109.

9、6691.69 12012.162882.48627.8110.7772.84 12254.493077.46729.1111.5846.81 12432.253244.65总和170.7759.34243.05 82395.11 18567.38平均24.38571108.4714286SUMMARY OUTPUT回归统计Multiple R 0.999752712R Square0.999505486Adjusted R Square0.999406583标准误差0.056916528观测值7方差分析dfSSMSF Significance F回归分析1 32.73809 32.73809

10、 10105.94 1.85E-09残差5 0.016197 0.003239总计6 32.75429Coefficients 标准误差t StatP-value Lower 95%Upper 95% 下限 95.0%Intercept92.91137938 0.156271 594.5544 2.55E-13 92.50967 93.31309 92.50967X Variable 1 0.638080517 0.006347 100.5283 1.85E-09 0.621764 0.654397 0.6217644.2T/Kc/%lnTlnc27320 2.4361631.30103SUM

11、MARY OUTPUT28325 2.4517861.3979429331 2.466868 1.491362回归统计浓度与沸点温度之间的关系32272217102104106108110112c/%T/Series131334 2.495544 1.531479Multiple R 0.98771533346 2.522444 1.662758R Square0.9755835358 2.547775 1.763428Adjusted R Square0.969475标准误差 0.029578观测值6方差分析dfSS回归分析1 0.139805残差4 0.003499总计5 0.143305

12、Coefficients 标准误差Intercept -8.14190.76478X Variable 13.887206 0.307502SUMMARY OUTPUT回归统计Multiple R 0.987714594R Square0.97558012Adjusted R Square0.969475149标准误差0.029578225观测值6方差分析dfSSMSF Significance F回归分析1 0.139805 0.139805159.801 0.000225残差4 0.003499 0.000875总计5 0.143305Coefficients 标准误差t StatP-va

13、lue Lower 95%Upper 95% 下限 95.0%Intercept -8.1418961590.76478 -10.6461 0.000441 -10.2653 -6.01853 -10.2653X Variable 13.88720636 0.307502 12.64124 0.000225 3.033444 4.740969 3.0334440.0002913.8872064.3某物质的溶解度与绝对温度之间的关系100010010100T/Kc/Series1试验号煎煮时间/min(x1)煎煮次数(x2)加水量/倍(x3)含量/(mg/L)y13018152402113735

14、03746460110265702634680395779031257SUMMARY OUTPUT回归统计Multiple R 0.992299718R Square0.984658731Adjusted R Square0.969317462标准误差2.742554455观测值7方差分析dfSSMSF Significance F回归分析3 1448.292 482.7641 64.18366 0.003211残差3 22.56481 7.521605总计6 1470.857Coefficients 标准误差t StatP-value Lower 95%Upper 95% 下限 95.0%I

15、ntercept -12.61111111 5.352918 -2.35593 0.099767 -29.6465 4.424264 -29.6465X Variable 10.175 0.066911 2.615396 0.079315 -0.03794 0.387942 -0.03794X Variable 2 13.71296296 1.561268 8.783223 0.003109 8.744312 18.68161 8.744312X Variable 3 1.287037037 0.5371472.39606 0.096215 -0.42241 2.996479 -0.42241

16、4.4试验号T/Na2O(x1)/% siO2(x2)/% CaO(x3)/%X1=x1X2=x1x2X3=x31102914729.11410089.12101114728.1141008811410087.1410061473.38.8141026.28.859931473.36.8141026.26.8610041473.38.1141026.28.179671473.37.1141026.27.189991473.36.1141026.26.199921474.37.8141040.27.81098014747.11410367.11198014746.114

17、10366.11298414747.11410367.11396515716.11510656.114100615719.11510659.11598815727.11510807.11698415729.11510809.11796715728.11510808.11898715727.11510807.11997915728.11510808.12098815726.11510806.12196815738.11510958.12294015737.11510957.12395615736.11510956.12495615738.11510958.12592515736.11510956

18、.1SUMMARY OUTPUT回归统计Multiple R 0.866175908R Square0.750260704Adjusted R Square0.714583661标准误差12.79120464观测值25方差分析dfSSMSF Significance F回归分析3 10322.09 3440.696 21.02923 1.57E-06残差21 3435.913 163.6149总计2413758Coefficients 标准误差t StatP-value Lower 95%Upper 95% 下限 95.0%Intercept1557.058911 96.99556 16.05

19、289 2.89E-13 1355.346 1758.772 1355.346X Variable 1 38.64532374 15.36278 2.515516 0.020093 6.696666 70.59398 6.696666X Variable 2-1.121266308 0.249355 -4.49666 0.000198 -1.63983-0.6027 -1.63983X Variable 3 6.484236525 2.688135 2.4121690.02509 0.893954 12.07452 0.893954所以得到的线性回归方程表达式为：y=1557.06+38.65

20、x1-1.12x1x2+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。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，

21、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=393.787.5.2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。5.4黄金分割法首先在实验范围

22、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.

23、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。9080706050403020100020406080100120y = -0.2274x2 + 32.1207x - 1032.7519电解质温度电解率)()()()()()(212131323212221321232232214xxyxxyxxyxxyxxyxxyx-+-+-+-+-=5.5对开法在直角坐标系中画出一矩形代表优选范围：20

24、 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xx2x3x4又x3x4对应的偏回归系数不显著，故归入残差项，重新进行回归分析如下：SUMMARY OUTPUT回归统计Multiple R 0.986424302R Square0.973032904Adjusted R Square0.964043872标准误差2.046677524观测值9方差分析dfSSMSF Significance F回归分析2 906.8667 453.4

25、333 108.2467 1.96E-05残差6 25.13333 4.188889总计8932Coefficients 标准误差t StatP-value Lower 95%Upper 95% 下限 95.0%Intercept20.39333333 2.549736 7.998213 0.000204 14.15435 26.63231 14.15435丙烯酸用量x1/mL1.720.12204 14.09371 7.97E-06 1.421378 2.018622 1.421378引发剂用量x2/%-10.33333333 3.051007 -3.38686 0.014733 -17.7

26、989 -2.86779 -17.7989简化后的方程非常显著，两偏回归系数也都显著，所以得到最终的二元线性方程：y=y=18.585+1.644x1-11.667x27.2序号废弃塑料质量x1/kg改性剂用量x2/kg增塑剂用量x3/kg混合剂用量x4/kgx1x2x3x3附着力评分y114712589814440216101868160324453181355623425904205146610019641522819541763614062411864264649072615165239025687828620621684004093091050270100481032121760384

27、289100SUMMARY OUTPUT回归统计Multiple R 0.997692974R Square0.995391271Adjusted R Square0.986173814标准误差3.039793997观测值10方差分析dfSSMSF Significance F回归分析6 5987.179 997.8632 107.9898 0.001361残差3 27.72104 9.240348总计96014.9Coefficients 标准误差t StatP-value Lower 95%Upper 95% 下限 95.0%Intercept275.8513061 46.78305 5.

28、896394 0.009738 126.9668 424.7359 126.9668废弃塑料质量x1/kg-9.164049588 1.288022 -7.11482 0.005714 -13.2631 -5.06499 -13.2631改性剂用量x2/kg-21.90324594 3.378473 -6.48318 0.007449 -32.6551 -11.1514 -32.6551增塑剂用量x3/kg-21.1426109 2.603757 -8.12004 0.003905 -29.4289 -12.8563 -29.4289混合剂用量x4/kg1.402877792 0.191033

29、 7.343644 0.005218 0.7949262.01083 0.794926x1x21.16458603 0.138149 8.429919 0.003503 0.724934 1.604238 0.724934x3x30.727523817 0.0975817.45562 0.004996 0.416979 1.038069 0.416979回归方程： y=275.851-9.164x1-21.903x2-21.143x3+1.403x4+1.16x1x2+0.73x32因素主次 x1x2x3x4x1x2方程非常显著，偏回归系数也非常显著，所以四个因素对试验结果都有非常显著地影响。

30、下面用规划求解来求得最大值x114127.179x25x35x468第八章习题答案8.1试验号z1z2z1z2z3z1z3灰化温度x1/原子化温度x2/11111170024002111-1-1700240031-1-111700180041-1-1-1-170018005-11-11-130024006-11-1-1130024007-1-111-130018008-1-11-113001800SUMMARY OUTPUT回归统计Multiple R 0.994230144R Square0.988493579Adjusted R Square0.959727528标准误差0.0079056

31、94观测值8方差分析dfSSMSF Significance F显著性z110.000761 0.000761 9.51E-05z210.009113 0.009113 0.001139*z310.000181 0.000181 2.26E-05z1z210.000264 0.000264 3.31E-05z1z310.000420.00042 5.26E-05回归分析5 0.010739 0.00214834.3632 0.028518*残差2 0.000125 6.25E-05总计7 0.010864Coefficients 标准误差t StatP-value Lower 95%Upper

32、 95% 下限 95.0%Intercept0.50475 0.002795 180.5848 3.07E-05 0.492724 0.516776 0.492724z10.00975 0.002795 3.488266 0.073266 -0.00228 0.021776 -0.00228z20.03375 0.002795 12.07477 0.006789 0.021724 0.045776 0.021724z1z20.00475 0.002795 1.699412 0.231342 -0.00728 0.016776 -0.00728z3-0.00575 0.002795 -2.057

33、18 0.175939 -0.01778 0.006276 -0.01778z1z30.00725 0.002795 2.593839 0.122018 -0.00478 0.019276 -0.00478回归方程： y=0.50475+0.00975z1+0.03375z2+0.00475z1z2-0.00575z3+0.00725z1z3由该回归方程中偏回归系数绝对值的大小，可以得到各因素和交互作用的主次顺序为：x2x1x1x3x3x1x2由方差分析的结果可知，只有z2因素对试验指标有非常显著的影响，故可把其他因素归入残差项，重新进行方差分析得到如下表：第二次方差分析表dfSSMSF显著性

34、z210.009113 0.009113 33.62546 *残差e6 0.001626 0.000271总计7 0.010864因素z2对试验指标y有非常显著的影响，因此回归方程可以简化为：y=0.50475+0.03375z2又z2=(x2-2100)/300,回带得方程y=0.2685+0.0001125x28.2试验号z1z2z3提取率y/%11118211-17.331-116.941-1-16.45-1116.96-11-16.57-1-1168-1-1-15.190006.6100006.5110006.6SUMMARY OUTPUT回归统计Multiple R 0.990265

35、441R Square0.980625644Adjusted R Square0.972322348标准误差0.121074733观测值11方差分析dfSSMSF Significance F显著性z112.101252.10125#DIV/0!*z212.311252.31125#DIV/0!*z310.781250.78125#DIV/0!*回归分析35.193751.73125 118.1008 2.34E-06*残差7 0.102614 0.014659总计10 5.296364Coefficients 标准误差t StatP-value Lower 95%Upper 95% 下限 9

36、5.0%Intercept6.618181818 0.036505 181.29324.1E-146.53186 6.7045036.53186z10.5125 0.042806 11.97251 6.46E-06 0.411279 0.613721 0.411279z20.5375 0.042806 12.55654 4.69E-06 0.436279 0.638721 0.436279z30.3125 0.042806 7.300313 0.000163 0.211279 0.413721 0.211279回归方程： y=6.618+0.5125z1+0.5375z2+0.3125z3由该

37、回归方程中偏回归系数绝对值的大小，可以得到各因素和交互作用的主次顺序为：x3x1x2由方差分析的结果可知，z1z2z3三个因素对试验指标都有非常显著的影响，所建立的方程也非常显著。失拟性检验差异源SSdfMSFF0.1失拟（Lf）0.095946975 0.019189 5.7568189.25重复试验（e1）0.0066666672 0.003333由FLfx1x2由方差分析的结果可知，z1z2z3三个因素对试验指标都有非常显著的影响，所建立的方程也非常显著。0.02650.02610.0257793008880098100试试验验设设计计与与数数据据处处理理课课后后习习题题答答案案785.

38、45.37.26.5上限 95.0%93.313090.654397MSF Significance F0.139805159.801 0.0002250.000875t StatP-value Lower 95%Upper 95% 下限 95.0% 上限 95.0%-10.6461 0.000441 -10.2653 -6.01853 -10.2653 -6.0185312.64124 0.000225 3.033444 4.740969 3.033444 4.740969上限 95.0%-6.018534.740969上限 95.0%4.4242640.38794218.681612.996479Y=T10291011101610069931