例8-1

试验号z1z2z1z2z3

11111

2111-1

31-1-11

41-1-1-1

5-11-11

6-11-1-1

7-1-111

8-1-11-1

SUMMARY OUTPUT

R Square0.988493579

Adjusted R Squar0.959727528

标准误差0.007905694

观测值8

方差分析

df SS MS F

z110.00076050.000760512.168

z210.00911250.0091125145.8

z310.00018050.0001805 2.888

z1z210.00026450.0002645 4.232

z1z310.00042050.0004205 6.728

回归分析50.01073850.002147734.3632

残差20.000125 6.25E-05

总计70.0108635

Coefficients标准误差t Stat P-value

Intercept0.504750.002795085180.5848499 3.07E-05

z10.009750.002795085 3.4882660450.073266

z20.033750.00279508512.074767080.006789

z1z20.004750.002795085 1.6994116630.231342

z3-0.005750.002795085-2.0571825390.175939

z1z30.007250.002795085 2.5938388540.122018

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

第二次方差分析表

df SS MS F

z210.00911250.009112533.62546残差e'60.0016260.000271

总计70.0108635

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+0.0001125x2

例8-2

试验号z1z2z3提取率y/%

11118

211-17.3

31-11 6.9

41-1-1 6.4

5-111 6.9

6-11-1 6.5

7-1-116

8-1-1-1 5.1

9000 6.6

10000 6.5

11000 6.6 SUMMARY OUTPUT

R Square0.980625644

Adjusted R Squar0.972322348

标准误差0.121074733

观测值11

方差分析

df SS MS F z11 2.10125 2.10125143.3411

z21 2.31125 2.31125157.6667

z310.781250.7812553.29457回归分析3 5.19375 1.73125118.1008

残差70.1026136360.014659091

总计10 5.296363636

Coefficients标准误差t Stat P-value Intercept 6.6181818180.036505405181.2932012 4.1E-14

z10.51250.04280638211.97251374 6.46E-06

z20.53750.04280638212.5565388 4.69E-06

z30.31250.0428063827.3003132570.000163

回归方程：y=6.618+0.5125z1+0.5375z2+0.3125z3

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，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

失拟性检验

差异源SS df MS F

失拟（Lf）0.0959469750.019189394 5.756818

重复试验（e1）0.00666666720.003333333

由F Lf

回归方程的回带

z1=(x1-70)/10z2=(x2-70)/2z3=(x3-2)/1

整理后得：

y=-0.2818+0.05125x1+0.26875x2+0.3125x3

例8-3

试验号z1z2z1z2z1'

11110.367583

21-1-10.367583

3-11-10.367583

4-1-110.367583

5 1.078000.529667

6-1.078000.529667

70 1.0780-0.63242

80-1.0780-0.63242

9000-0.63242

10000-0.63242

∑zi2 6.324168 6.324168

SUMMARY OUTPUT

R Square0.99573215

Adjusted R Squar0.990397338

标准误差 3.484618488

观测值10

方差分析

df SS MS F

回归分析511331.929742266.385947186.648

残差448.5702640412.14256601

总计911380.5

Coefficients标准误差t Stat P-value

Intercept468.5 1.10193312425.1619191 1.84E-10

z19.089258856 1.385649972 6.559563410.002794

z2-26.5634942 1.385649972-19.17042163 4.36E-05

z1z20 1.74230924401

z1'0 2.1201341401

z2'-41.73590203 2.12013414-19.68550067 3.93E-05

回归方程：y=468.5+9.09z1-26.56z2+z3

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，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

z1z3灰化温度x1/原子化温度x灯电流x3/mA x1x2x1x3吸光度yi 1700240010168000070000.552

-170024008168000056000.554

1700180010126000070000.48

-170018008126000056000.472

-130024001072000030000.516

13002400872000024000.532

-130018001054000030000.448

13001800854000024000.484 Significance F显著性SST

0.010863

**

0.028518*

Lower 95%Upper 95%下限 95.0%上限 95.0%

0.4927240.5167760.4927240.516776

-0.002280.021776-0.002280.021776

0.0217240.0457760.0217240.045776

-0.007280.016776-0.007280.016776

-0.017780.006276-0.017780.006276

-0.004780.019276-0.004780.019276

00575z3+0.00725z1z3

作用的主次顺序为：x2>x1>x1x3>x3>x1x2

，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：

显著性

**

提取率y/%

Significance F显著性

**

**

**

2.34E-06**

Lower 95%Upper 95%下限 95.0%上限 95.0%

6.53186 6.704503 6.53186 6.704503

0.4112790.6137210.4112790.613721

0.4362790.6387210.4362790.638721

0.2112790.4137210.2112790.413721

次顺序为：x3>x1>x2

的影响，所建立的方程也非常显著。

F0.1

9.25

z2'y z12z22

0.36758342311

0.36758348611

0.36758341811

0.36758345411

-0.63242491 1.1620840

-0.63242472 1.1620840

0.5296674280 1.162084

0.5296674920 1.162084

-0.6324251200

-0.6324250900 Significance F

7.93E-05

Lower 95%Upper 95%下限 95.0%上限 95.0%

465.4405471.5595465.4405471.5595

5.24207812.93644 5.24207812.93644

-30.4107-22.7163-30.4107-22.7163

-4.83743 4.837426-4.837434.837426

-5.88644 5.886436-5.886445.886436

-47.6223-35.8495-47.6223-35.8495作用的主次顺序为：x3>x1>x2

的影响，所建立的方程也非常显著。