实验设计与数据处理第七章例题及课后习题答案
例7-1
水平丙烯酸用量x1/mL引发剂用量x2/%丙烯酸中和度x3/%
1120.464.5
214.50.686.5
3170.859
419.5181
5220.353.5
624.50.575.5
7270.748
829.50.970
932 1.192 SUMMARY OUTPUT
回归统计
Multiple R0.99300126
R Square0.986051502
Adjusted R 0.972103004
标准误差 1.802775638
观测值9
方差分析
df SS MS
回归分析4919229.75
残差413 3.25
总计8932
Coefficients标准误差t Stat
Intercept18.58484848 3.704122528 5.017341718
X Variable 1.6444444440.12668615812.98045869
X Variable -11.66666667 3.167153959-3.683643681
X Variable 0.1010101010.057584617 1.754116039
X Variable -3.333333333 2.111435972-1.578704435
回归方程：y=18.585+1.644x1-11.667x2+0.101x3-3.333x4
因素主次x1>x2>x3>x4
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 R0.986424302
R Square0.973032904
Adjusted R 0.964043872
标准误差 2.046677524
观测值9
方差分析
df SS MS
回归分析2906.8666667453.4333333
残差625.13333333 4.188888889
总计8932
Coefficients标准误差t Stat
Intercept20.39333333 2.549736377.998212511
丙烯酸用量x 1.720.12204026914.09370874
引发剂用量x-10.33333333 3.051006715-3.386860239
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+1.644x1-11.667x2
例7-2
序号废弃塑料质量x1/kg改性剂用量x2/kg增塑剂用量x3/kg
114712
2161018
318135
420514
522819
624118
7261516
828620
930910
10321217
SUMMARY OUTPUT
回归统计
Multiple R0.997692974
R Square0.995391271
Adjusted R 0.986173814
标准误差 3.039793997
观测值10
方差分析
df SS MS
回归分析65987.178957997.8631596
残差327.721042639.240347544
总计96014.9
Coefficients标准误差t Stat
Intercept275.851306146.78305189 5.896393993
废弃塑料质量-9.164049588 1.288022499-7.114821051
改性剂用量x-21.90324594 3.378473063-6.483179097
增塑剂用量x-21.1426109 2.60375725-8.120039186
混合剂用量x 1.4028777920.191032937.343643785
x1x2 1.164586030.138149138.429919396
x3x30.7275238170.0975805987.4556196
回归方程：y=275.851-9.164x1-21.903x2-21.143x3+1.403x4+1.16x1x2+032
因素主次x1x2>x3>x4>x1>x2
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
x114127.179
x25
x35
x468
甲醛用量x4/mL吸盐水倍率y
1.2534
1.142
0.9540
0.845
0.6555
0.559
0.3560
0.261
1.463
P-value Lower 95%Upper 95%下限 95.0%上限 95.0%
0.0073992188.30055628.869148.30055628.86914
0.000203236 1.292707 1.996182 1.292707 1.996182
0.021136245-20.4601-2.87324-20.4601-2.87324
0.154272871-0.058870.260891-0.058870.260891
0.189546861-9.19562 2.528953-9.19562 2.528953行回归分析如下：
P-value Lower 95%Upper 95%下限 95.0%上限 95.0%
0.00020371714.1543526.6323114.1543526.63231
7.9655E-06 1.421378 2.018622 1.421378 2.018622
0.014732564-17.7989-2.86779-17.7989-2.86779到最终的二元线性方程：
混合剂用量x4/kg x1x2x3x3附着力评分y
589814440
6816032445
562342590
6610019641
5417636140
642646490
5239025687
6216840040
5027010048
60384289100
F Significance F
107.98978660.001361
P-value Lower 95%Upper 95%下限 95.0%上限 95.0%
0.009738124126.9668424.7359126.9668424.7359
0.005713789-13.2631-5.06499-13.2631-5.06499
0.007449139-32.6551-11.1514-32.6551-11.1514
0.003904616-29.4289-12.8563-29.4289-12.8563
0.0052176970.794926 2.010830.794926 2.01083
0.0035028850.724934 1.6042380.724934 1.604238
0.0049955620.416979 1.0380690.416979 1.038069 1x2+0.73x32
都有非常显著地影响。