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2.10.04150.03550.03360.03120.03020.02890.0277Re175002550029700376004240050900618002.2x1234 Mx=1/x=20mmy88.28.38 My=1/y=5mm关系曲线0.10.01100001000000Rex与y的关系图4.543.532.521.510.507.87.988.18.28.38.4xy系列12.3发酵时间/d012345PH值 5.45.865.95.85.7残糖量/（g/l）24.513.311.210.19.58.
2、12.4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-201NKA-9AB-8D-4006D-101S-8NKA-02468101214161820树脂型号吸附量/(mg/g)x与y的关系图4.543.532.521.510.507.87.988.18.28.38.4xy系列12.5植物油凝固点/甲乙花生油2.93.5棉子油-6.
3、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/甲乙18115232122比例/%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DA-201NKA-9AB-8D-4006D-101S-8NKA-02468101214161820树脂型号吸附量/(mg/g)3.1第三章习题答案3.1颜色销售额/万元橘黄色26.528.725.1
4、29.127.2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-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）/（
5、L/min）89101112181.181.580.380771.581.481.879.479.175.927576.175.475.470.818115232122比例/%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.
6、95 27.89667列 44304.376.07521.4625列 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
7、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1.866666667 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 5.98737
8、8交互2.35521.1775 16.82143 0.003467 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3129272523211917102104106108110112c/%T/系列1ixyxi2yi2xiyi119.6105.4384.16 11109.162065.84220.5106420.25112362173322.3107.2497.29 11491.842390.56425
9、.1108.9630.01 11859.212733.39526.3109.6691.69 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
10、 Significance F回归分析1 32.73809 32.73809 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%Intercept92.91137938 0.156271 594.5544 2.55E-13 92.50967 93.31309X Variable 1 0.638080517 0.006347 100.5283 1.85E-09 0.621764 0.654397浓度与沸点温度之间的关系3129272523211917
11、102104106108110112c/%T/系列14.2T/Kc/%lnTlnc27320 2.4361631.30103SUMMARY OUTPUT28325 2.4517861.3979429331 2.466868 1.491362回归统计31334 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df回归分析1残差4总计5CoefficientsIn
12、tercept-8.1419X Variable 13.887206SUMMARY 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-value Lower 95%Upper 95%Intercept-8.14
13、18961590.76478-10.6461 0.000441-10.2653-6.01853X Variable 13.88720636 0.307502 12.64124 0.000225 3.033444 4.7409690.000291某物质的溶解度与绝对温度之间的关系100010010100T/Kc/系列13.8872064.3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Multiple R 0.99229
14、9718R 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%Intercept-12.61111111 5.352918-2.35593 0.099767-29.6465 4.424264X Variable 10.175
15、 0.066911 2.615396 0.079315-0.03794 0.387942X Variable 2 13.71296296 1.561268 8.783223 0.003109 8.744312 18.68161X Variable 3 1.287037037 0.5371472.39606 0.096215-0.42241 2.9964794.4试验号T/Na2O(x1)/%siO2(x2)/%CaO(x3)/%X1=x1X2=x1x21102914729.11410082101114728.11410083101614727.1141008410061473.38.81410
16、26.259931473.36.8141026.2610041473.38.1141026.279671473.37.1141026.289991473.36.1141026.299921474.37.8141040.21098014747.11410361198014746.11410361298414747.11410361396515716.115106514100615719.11510651598815727.11510801698415729.11510801796715728.11510801898715727.11510801997915728.1151080209881572
17、6.11510802196815738.11510952294015737.11510952395615736.11510952495615738.11510952592515736.1151095SUMMARY 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241
18、3758Coefficients 标准误差t StatP-value Lower 95%Upper 95%Intercept1557.058911 96.99556 16.05289 2.89E-13 1355.346 1758.772X Variable 1 38.64532374 15.36278 2.515516 0.020093 6.696666 70.59398X Variable 2-1.121266308 0.249355-4.49666 0.000198-1.63983-0.6027X Variable 3 6.484236525 2.688135 2.4121690.0250
19、9 0.893954 12.07452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。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-
20、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=393.787.5.2电解质温度657480电解率94.398.981.5目标函数1
21、01.4993 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的0.618处做第一个实验，这一点的碱液用量为9080706050403020100020406080100120y=-0.2274x2+32.1207x-1032.7519电解质温度电解率)()()()()()(212131323212221321232232214xxyxxyxxyxxyxxyxxyxx1=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
22、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
23、，则为最佳点。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
24、Significance F回归分析2 906.8667 453.4333 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%Intercept20.39333333 2.549736 7.998213 0.000204 14.15435 26.63231丙烯酸用量x1/mL1.720.12204 14.09371 7.97E-06 1.421378 2.018622引发剂用量x2/%-10.33333333 3.051007-3.38686 0.014733
25、-17.7989-2.86779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/kgx1x2x3x3114712589814421610186816032431813556234254205146610019652281954176361624118642646472615165239025682862062168400930910502701001032121760384289SUMMARY OUTPUT回归统计Multiple
26、 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%Intercept275.8513061 46.78305 5.896394 0.009738 126.9668 424.7359废弃塑料质量x1
27、/kg-9.164049588 1.288022-7.11482 0.005714-13.2631-5.06499改性剂用量x2/kg-21.90324594 3.378473-6.48318 0.007449-32.6551-11.1514增塑剂用量x3/kg-21.1426109 2.603757-8.12004 0.003905-29.4289-12.8563混合剂用量x4/kg1.402877792 0.191033 7.343644 0.005218 0.7949262.01083x1x21.16458603 0.138149 8.429919 0.003503 0.724934 1
28、.604238x3x30.727523817 0.0975817.45562 0.004996 0.416979 1.038069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。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x1/1111117002111-1-170031-1-11170041-1-1-1-17005-
29、11-11-13006-11-1-113007-1-111-13008-1-11-11300SUMMARY OUTPUT回归统计Multiple R 0.994230144R Square0.988493579Adjusted R Square0.959727528标准误差0.007905694观测值8方差分析dfSSMSF Significance Fz110.000761 0.000761 9.51E-05z210.009113 0.009113 0.001139z310.000181 0.000181 2.26E-05z1z210.000264 0.000264 3.31E-05z1z3
30、10.000420.00042 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 95%Intercept0.50475 0.002795 180.5848 3.07E-05 0.492724 0.516776z10.00975 0.002795 3.488266 0.073266-0.00228 0.021776z20.03375 0.002795 12.07477 0.006789 0.02
31、1724 0.045776z1z20.00475 0.002795 1.699412 0.231342-0.00728 0.016776z3-0.00575 0.002795-2.05718 0.175939-0.01778 0.006276z1z30.00725 0.002795 2.593839 0.122018-0.00478 0.019276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：由方差分析的结果可知，只有z2因素对
32、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/%11118211-17.331-116.941-1-16.45-1116.96-11-16.57-1-1168-1-1-15.1900
33、06.6100006.5110006.6SUMMARY OUTPUT回归统计Multiple R 0.990265441R Square0.980625644Adjusted R Square0.972322348标准误差0.121074733观测值11方差分析dfSSMSF Significance Fz112.101252.10125#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%Intercept6.618181818 0.036505 181.29324.1E-146.53186 6.
