实验设计与数据处理第三四五章例题及课后习题答案.xls

1、例4-5 试验号 x1 x2 x3 y y21 1 13 1.5 0.33 0.10892 1.4 19 3 0.336 0.1128963 1.8 25 1 0.294 0.0864364 2.2 10 2.5 0.476 0.2265765 2.6 16 0.5 0.209 0.0436816 3 22 2 0.451 0.2034017 3.4 28 3.5 0.482 0.232324总和 15.4 133 14 2.578 1.014214平均 2.2 19 20.368286L11 4.48 方程 目标函数L22 252 1 1E-06 1E-06L33 7 2 1E-06L12

2、16.8 32.32E-09L23 10.5 47.24E-11L31 1.4L1y 0.2404 于是 三元线性回归方程为：y=0.197+0.0455x1-0.00377x2+0.0715x3L2y 0.564L3y 0.5245检验线性回归方程的显著性 方差分析表（1）F检验 SSt 0.064773429 差异源SSr 0.046300406 回归Sse 0.018473023 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y y21 70 10 1 7.6 57.762 70 10 3 10.3 106.093 70 30 1 8.9 79.214

3、 70 30 3 11.2 125.445 90 10 1 8.4 70.566 90 10 3 11.1 123.217 90 30 1 9.8 96.048 90 30 3 12.6 158.76SUM 640 160 16 79.9 817.07AVE 80 20 2 9.9875SUMMARY OUTPUT回归统计Multiple R 0.99645389R Square 0.992920354Adjusted R Square0.987610619标准误差 0.183711731观测值 8方差分析df SS MS F Significance F回归分析 3 18.93375 6.3

4、1125 187 9.37555E-05残差 4 0.135 0.03375总计 7 19.06875Coefficients 标准误差 t Stat P-value Lower 95%Intercept 2.1875 0.554949322 3.9418013740.016934 0.646713671X Variable 1 0.04875 0.006495191 7.5055534990.001686 0.03071646X Variable 2 0.06375 0.006495191 9.8149545760.000604 0.04571646X Variable 3 1.3125 0

5、.064951905 20.207259423.54E-05 1.132164601所以得到的线性回归方程表达式为：y=2.1875+0.04875x1+0.06375x2+1.3125x3L11 800L22 800L33 8P1 0.315761009P2 0.412918242P3 0.850125793t1 7.505553499t2 9.814954576t3 20.20725942例4-7p/atm 2.01 1.78 1.75 1.73 1.68M/(mol/min) 0.763 0.715 0.71 0.695 0.698p/atm M/(mol/min)x yxi2 yi2l

6、g(pi) lg(Mi)1 2.01 0.763 0.303196057 -0.1174754620.091928 0.0138004842 1.78 0.715 0.250420002 -0.145693958 0.06271 0.0212267293 1.75 0.71 0.243038049 -0.1487416510.059067 0.0221240794 1.73 0.695 0.238046103 -0.1580151950.056666 0.0249688025 1.68 0.698 0.225309282 -0.1561445770.050764 0.0243811296 1.

7、62 0.673 0.209515015 -0.1719849360.043897 0.0295788187 1.4 0.63 0.146128036 -0.2006594510.021353 0.0402642158 1.36 0.612 0.133538908 -0.2132485780.017833 0.0454749569 0.93 0.498 -0.031517051 -0.3027706570.000993 0.09167007110 0.53 0.371 -0.27572413 -0.430626090.076024 0.18543883SUM 14.79 6.365 1.441

8、95027 -2.0453605560.481235 0.498928113AVE 1.479 0.6365 0.144195027 -0.204536056SUMMARY OUTPUT回归统计Multiple R 0.999492866R Square 0.998985989Adjusted R Square0.998859237标准误差 0.00319584观测值 10方差分析 F0.01(1,8)=11.3df SS MS F Significance F回归分析 1 0.080496426 0.0804964267881.459 2.89205E-13残差 8 8.17071E-05

9、1.02134E-05总计 9 0.080578133Coefficients 标准误差 t Stat P-value Lower 95%Intercept -0.282790341 0.001341014 -210.8779792.86E-16 -0.285882725X Variable 10.542697532 0.006113002 88.777581472.89E-13 0.528600925例4-8xi 1 3 4 5 6yi 2 7 8 10 11i xi yi x1 x2 y y21 1 2 1 1 2 42 3 7 3 9 7 493 4 8 4 16 8 644 5 10

10、5 25 10 1005 6 11 6 36 11 1216 7 12 7 49 12 1447 8 10 8 64 10 1008 9 9 9 81 9 819 10 8 10 100 8 64SUM 53 77 53 381 77 727AVE 5.888889 8.555555556 5.888888889 42.333333338.5555561 21 086420024681 01 21 4xy Series1SUMMARY OUTPUT回归统计Multiple R 0.981636002R Square 0.96360924Adjusted R Square0.951478987标

11、准误差 0.643254553观测值 9方差分析 F0.01(2,6)=10.92df SS MS F Significance F回归分析 2 65.7395637 32.8697818579.43851 4.81918E-05残差 6 2.482658518 0.41377642总计 8 68.22222222Coefficients 标准误差 t Stat P-value Lower 95%Intercept -1.715966387 0.846062418 -2.0281794220.088888 -3.786206541X Variable 13.750076394 0.330019

12、174 11.363207642.78E-05 2.942548569X Variable 2-0.279029794 0.028576121 -9.7644392726.63E-05 -0.348953042例4-9i x1 x2 x3 y X1=x31 1 13 1.5 0.33 1.52 1.4 19 3 0.336 33 1.8 25 1 0.294 14 2.2 10 2.5 0.476 2.55 2.6 16 0.5 0.209 0.56 3 22 2 0.451 27 3.4 28 3.5 0.482 3.5sum 15.4 133 14 2.578 14SUMMARY OUTP

13、UT回归统计Multiple R 0.9838125691 21 086420024681 01 21 4xy Series1R Square 0.967887171Adjusted R Square0.935774341标准误差 0.026331591观测值 7方差分析 F0.05(3,3)=9.28df SS MS F Significance F回归分析 3 0.062693371 0.02089779 30.1402 0.00967471残差 3 0.002080058 0.000693353总计 6 0.064773429Coefficients 标准误差 t Stat P-valu

14、e Lower 95%Intercept 0.057886497 0.042352824 1.366768280.265114 -0.076899093X Variable 10.252172538 0.047467569 5.3125227190.013025 0.101109549X Variable 2-0.064840835 0.012883654 -5.0327985030.015119 -0.105842372X Variable 30.028317025 0.005824205 4.8619554570.016617 0.009781806习题3.1颜色 销售额/万元橘黄色 26

15、.5 28.7 25.1 29.1 27.2粉色 31.2 28.3 30.8 27.9 29.6绿色 27.9 25.1 28.5 24.2 26.5无色 30.8 29.6 32.4 31.7 32.8方差分析：单因素方差分析SUMMARY组 观测数 求和 平均 方差行 1 5 136.6 27.32 2.672行 2 5 147.8 29.56 2.143行 3 5 132.2 26.44 3.298行 4 5 157.3 31.46 1.658方差分析差异源 SS df MS F P-value组间 76.8455 3 25.61516667 10.4862 0.00046614组内

16、39.084 16 2.44275总计 115.9295 19习题3.2乙炔流量 空气流量/（L/min）/（L/min） 8 9 10 11 121 81.1 81.5 80.3 80 771.5 81.4 81.8 79.4 79.1 75.92 75 76.1 75.4 75.4 70.82.5 60.4 67.9 68.7 69.8 68.7方差分析：无重复双因素分析SUMMARY 观测数 求和 平均 方差行 1 5 399.9 79.98 3.137行 2 5 397.6 79.52 5.507行 3 5 372.7 74.54 4.528行 4 5 335.5 67.1 14.48

17、5列 1 4 297.9 74.475 96.7425列 2 4 307.3 76.825 42.2625列 3 4 303.8 75.9527.89667列 4 4 304.3 76.075 21.4625列 5 4 292.4 73.1 15.9方差分析差异源 SS df MS F P-value行 537.6375 3 179.212528.61486 9.44035E-06列 35.473 4 8.868251.415994 0.287422317误差 75.155 12 6.262916667总计 648.2655 19习题3.3铝材材质去离子水 自来水1 2.3 5.61 1.8

18、5.32 1.5 5.32 1.5 4.83 1.8 7.43 2.3 7.4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 2 2 4求和 4.1 10.9 15平均 2.05 5.45 3.75方差 0.125 0.045 3.912观测数 2 2 4求和 3 10.1 13.1平均 1.5 5.05 3.275方差 0 0.125 4.24253观测数 2 2 4求和 4.1 14.8 18.9平均 2.05 7.4 4.725方差 0.125 0 9.5825总计观测数 6 6求和 11.2 35.8平均 1.866666667 5.966666667方差 0

19、.130666667 1.298666667方差分析差异源 SS df MS F P-value样本 4.371666667 2 2.18583333331.22619 0.000673423列 50.43 1 50.43720.4286 1.76634E-07交互 2.355 2 1.177516.82143 0.00346704内部 0.42 6 0.07总计 57.57666667 11习题4.1c/%(x) T/（y)19.6 105.420.5 10622.3 107.225.1 108.926.3 109.627.8 110.729.1 111.5浓 度 与 沸 点 温 度 之 间

20、 的 关 系32272217102104106108110112c/%T/S eries1i x y xi2 yi2 xiyi1 19.6 105.4 384.16 11109.16 2065.842 20.5 106 420.25 11236 21733 22.3 107.2 497.29 11491.84 2390.564 25.1 108.9 630.01 11859.21 2733.395 26.3 109.6 691.69 12012.16 2882.486 27.8 110.7 772.84 12254.49 3077.467 29.1 111.5 846.81 12432.25

21、3244.65总和 170.7 759.3 4243.05 82395.1118567.38平均 24.38571 108.4714286SUMMARY OUTPUT回归统计Multiple R 0.999752712R Square 0.999505486Adjusted R Square0.999406583标准误差 0.056916528观测值 7方差分析df SS MS F Significance F回归分析 1 32.73808826 32.7380882610105.94 1.84673E-09残差 5 0.016197456 0.003239491总计 6 32.7542857

22、1Coefficients 标准误差 t Stat P-value Lower 95%Intercept 92.91137938 0.156270601 594.5544392.55E-13 92.50967302X Variable 10.638080517 0.006347274 100.52828121.85E-09 0.621764331浓 度 与 沸 点 温 度 之 间 的 关 系32272217102104106108110112c/%T/S eries1习题4.2T/K c/% lnT lnc273 20 2.436162647 1.301029996 SUMMARY OUTPU

23、T283 25 2.451786436 1.397940009293 31 2.46686762 1.491361694 回归统计313 34 2.495544338 1.531478917 Multiple R333 46 2.522444234 1.662757832 R Square353 58 2.547774705 1.763427994 Adjusted R Square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 R 0.987714594R Square 0.97558012Adjusted

24、 R Square0.969475149标准误差 0.029578225观测值 6方差分析df SS MS F Significance F回归分析 1 0.13980529 0.13980529 159.801 0.00022547残差 4 0.003499485 0.000874871总计 5 0.143304776Coefficients 标准误差 t Stat P-value Lower 95%某 物 质 的 溶 解 度 与 绝 对 温 度 之 间 的 关 系100010010100T/Kc/S eries1Intercept -8.141896159 0.764779948 -10.

25、646063850.000441 -10.2652657X Variable 1 3.88720636 0.307501966 12.641240680.000225 3.0334440320.0002910853.88720636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)y1 30 1 8 152 40 2 11 373 50 3 7 464 60 1 10 265 70 2 6 346 80 3 9 577 90 3 12 57SUMMARY OUTPUT回归统计Multiple R 0.992299718R Square 0.984

26、658731Adjusted R Square0.969317462标准误差 2.742554455观测值 7方差分析df SS MS F Significance F回归分析 3 1448.292328 482.764109364.18366 0.003210937残差 3 22.56481481 7.521604938总计 6 1470.857143Coefficients 标准误差 t Stat P-value Lower 95%Intercept -12.61111111 5.352918185 -2.3559319750.099767 -29.64648581X Variable 1 0.175 0.066911477 2.6153958490.079315 -0.037942184X Variable 213.71296296 1.561267804 8.7832227930.003109 8.744312009X Variable 31.287037037 0.537147255 2.3960599720.096215 -0.42240526