试验设计与数据处理第二版课后习题答案表格文件下载.xls
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试验设计与数据处理第二版课后习题答案表格文件下载.xls
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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34303.875.9527.89667列44304.376.07521.4625列54292.473.115.9方差分析差异源SSdfMSFP-valueFcrit行537.63753179.212528.614869.44E-063.490295列35.47348.868251.4159940.2874223.259167误差75.155126.262917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1.8666666675.966667方差0.1306666671.298667方差分析差异源SSdfMSFP-valueFcrit样本4.37166666722.18583331.226190.0006735.143253列50.43150.43720.42861.77E-075.987378交互2.35521.177516.821430.0034675.143253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1ixyxi2yi2xiyi119.6105.4384.1611109.162065.84220.5106420.25112362173322.3107.2497.2911491.842390.56425.1108.9630.0111859.212733.39526.3109.6691.6912012.162882.48627.8110.7772.8412254.493077.46729.1111.5846.8112432.253244.65总和170.7759.34243.0582395.1118567.38平均24.38571108.4714286SUMMARYOUTPUT回归统计MultipleR0.999752712RSquare0.999505486AdjustedRSquare0.999406583标准误差0.056916528观测值7方差分析dfSSMSFSignificanceF回归分析132.7380932.7380910105.941.85E-09残差50.0161970.003239总计632.75429Coefficients标准误差tStatP-valueLower95%Upper95%Intercept92.911379380.156271594.55442.55E-1392.5096793.31309XVariable10.6380805170.006347100.52831.85E-090.6217640.654397浓度与沸点温度之间的关系3129272523211917102104106108110112c/%T/系列14.2T/Kc/%lnTlnc273202.4361631.30103SUMMARYOUTPUT283252.4517861.39794293312.4668681.491362回归统计313342.4955441.531479MultipleR0.987715333462.5224441.662758RSquare0.97558353582.5477751.763428AdjustedRSquare0.969475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5CoefficientsIntercept-8.1419XVariable13.887206SUMMARYOUTPUT回归统计MultipleR0.987714594RSquare0.97558012AdjustedRSquare0.969475149标准误差0.029578225观测值6方差分析dfSSMSFSignificanceF回归分析10.1398050.139805159.8010.000225残差40.0034990.000875总计50.143305Coefficients标准误差tStatP-valueLower95%Upper95%Intercept-8.1418961590.76478-10.64610.000441-10.2653-6.01853XVariable13.887206360.30750212.641240.0002253.0334444.7409690.000291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)y1301815240211373503746460110265702634680395779031257SUMMARYOUTPUT回归统计MultipleR0.992299718RSquare0.984658731AdjustedRSquare0.969317462标准误差2.742554455观测值7方差分析dfSSMSFSignificanceF回归分析31448.292482.764164.183660.003211残差322.564817.521605总计61470.857Coefficients标准误差tStatP-valueLower95%Upper95%Intercept-12.611111115.352918-2.355930.099767-29.64654.424264XVariable10.1750.0669112.6153960.079315-0.037940.387942XVariable213.712962961.5612688.7832230.0031098.74431218.68161XVariable31.2870370370.5371472.396060.096215-0.422412.9964794.4试验号T/Na2O(x1)/%siO2(x2)/%CaO(x3)/%X1=x1X2=x1x21102914729.11410082101114728.11410083101614727.1141008410061473.38.8141026.259931473.36.8141026.2610041473.38.1141026.279671473.37.1141026.289991473.36.1141026.299921474.37.8141040.21098014747.11410361198014746.11410361298414747.11410361396515716.115106514100615719.11510651598815727.11510801698415729.11510801796715728.11510801898715727.11510801997915728.11510802098815726.11510802196815738.11510952294015737.11510952395615736.11510952495615738.11510952592515736.1151095SUMMARYOUTPUT回归统计MultipleR0.866175908RSquare0.750260704AdjustedRSquare0.714583661标准误差12.79120464观测值25方差分析dfSSMSFSignificanceF回归分析310322.093440.69621.029231.57E-06残差213435.913163.6149总计2413758Coefficients标准误差tStatP-valueLower95%Upper95%Intercept1557.05891196.9955616.052892.89E-131355.3461758.772XVariable138.6453237415.362782.5155160.0200936.69666670.59398XVariable2-1.1212663080.249355-4.496660.000198-1.63983-0.6027XVariable36.4842365252.6881352.4121690.025090.89395412.07452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-(420-370.56)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101.4993x=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。
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:
SUMMARYOUTPUT回归统计MultipleR0.986424302RSquare0.973032904AdjustedRSquare0.964043872标准误差2.046677524观测值9方差分析dfSSMSFSignificanceF回归分析2906.8667453.4333108.24671.96E-05残差625.133334.188889总计8932Coefficients标准误差tStatP-valueLower95%Upper95%Intercept20.393333332.5497367.9982130.00020414.1543526.63231丙烯酸用量x1/mL1.720.1220414.093717.97E-061.4213782.018622引发剂用量x2/%-10.333333333.051007-3.386860.014733-17.7989-2.86779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/kgx1x2x3x3114712589814421610186816032431813556234254205146610019652281954176361624118642646472615165239025682862062168400930910502701001032121760384289SUMMARYOUTPUT回归统计MultipleR0.997692974RSquare0.995391271AdjustedRSquare0.986173814标准误差3.039793997观测值10方差分析dfSSMSFSignificanceF回归分析65987.179997.8632107.98980.001361残差327.721049.240348总计96014.9Coefficients标准误差tStatP-valueLower95%Upper95%Intercept275.851306146.783055.8963940.009738126.9668424.7359废弃塑料质量x1/kg-9.1640495881.288022-7.114820.005714-13.2631-5.06499改性剂用量x2/kg-21.903245943.378473-6.483180.007449-32.6551-11.1514增塑剂用量x3/kg-21.14261092.603757-8.120040.003905-29.4289-12.8563混合剂用量x4/kg1.4028777920.1910337.3436440.0052180.7949262.01083x1x21.164586030.1381498.4299190.0035030.7249341.604238x3x30.7275238170.0975817.455620.0049960.4169791.038069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x1/1111117002111-1-170031-1-11170041-1-1-1-17005-11-11-13006-11-1-113007-1-111-13008-1-11-11300SUMMARYOUTPUT回归统计MultipleR0.994230144RSquare0.988493579AdjustedRSquare0.959727528标准误差0.007905694观测值8方差分析dfSSMSFSignificanceFz110.0007610.0007619.51E-05z210.0091130.0091130.001139z310.0001810.0001812.26E-05z1z210.0002640.0002643.31E-05z1z310.000420.000425.26E-05回归分析50.0107390.00214834.36320.028518残差20.0001256.25E-05总计70.010864Coefficients标准误差tStatP-valueLower95%Upper95%Intercept0.504750.002795180.58483.07E-050.4927240.516776z10.009750.0027953.4882660.073266-0.002280.021776z20.033750.00279512.074770.0067890.0217240.045776z1z20.004750.0027951.6994120.231342-0.007280.016776z3-0.005750.002795-2.057180.175939-0.017780.006276z1z30.007250.0027952.5938390.122018-0.004780.019276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z210.0091130.00911333.62546*残差e60.0016260.000271总计70.010864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/%11118211-17.331-116.941-1-16.45-1116.96-11-16.57-1-1168-1-1-15.190006.6100006.5110006.6SUMMARYOUTPUT回归统计MultipleR0.990265441RSquare0.980625644AdjustedRSquare0.972322348标准误差0.121074733观测值11方差分析dfSSMSFSignificanceFz112.101252.10125#DIV/0!
z212.311252.31125#DIV/0!
z310.781250.78125#DIV/0!
回归分析35.193751.73125118.10082.34E-06残差70.1026140.014659总计105.296364Coefficients标准误差tStatP-valueLower95%Upper95%Intercept6.6181818180.036505181.29324.1E-146.531866.
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