（高手请进）这个数据的分析
对以下的数据（红色部分）进行分析，其中HotBarT、DwelTime、HotBarP、MatTemp是因子，Strength、VarStrength是响应变量，初步分析结果如蓝色部分，讨论的问题是：
1.是否需要精简回归模型呢？也就是将回归项剔除，如果要剔除，应该怎样综合两个响应变量来考虑逐步剔出呢？:)
2.回归检验的方差分析中Lack-of-Fit的P值为0，代表什么意思呢，是否说明方程无效呢？:D
3.两个回归方程的RSQ都只有70%多，这代表什么意思呢，说明方程拟合不好，还是另外存在显著的因子抑或是其它原因。
HotBarT DwelTime HotBarP MatTemp Strength VarStrength
150 0.50 50 70 10.5010 4.46000
200 0.50 50 70 26.7490 0.80000
150 1.00 50 70 15.6990 0.99400
200 1.00 50 70 8.2510 6.74600
150 0.50 150 70 12.0010 2.99600
200 0.50 150 70 28.4010 0.84000
150 1.00 150 70 21.5990 2.13800
200 1.00 150 70 13.7030 4.49400
150 0.50 50 110 12.2010 4.14400
200 0.50 50 110 27.6490 1.07600
150 1.00 50 110 19.7990 2.69000
200 1.00 50 110 12.4470 5.28200
150 0.50 150 110 15.7010 3.54000
200 0.50 150 110 30.3010 3.45200
150 1.00 150 110 23.2990 2.21400
200 1.00 150 110 15.6990 6.49000
125 0.75 100 90 20.6865 1.34636
225 0.75 100 90 24.7047 1.63296
175 0.25 100 90 25.5021 1.49727
175 1.25 100 90 21.3752 2.92266
175 0.75 0 90 25.9942 0.83801
175 0.75 200 90 30.0581 1.14190
175 0.75 100 50 27.4284 1.69595
175 0.75 100 130 30.0516 2.58797
175 0.75 100 90 28.5000 0.94000
175 0.75 100 90 28.2000 0.91000
175 0.75 100 90 27.4000 0.97000
175 0.75 100 90 28.9000 0.86000
175 0.75 100 90 28.3000 0.83000
175 0.75 100 90 28.7000 0.92000
175 0.75 100 90 29.1000 0.95000
Response Surface Regression: Strength versus HotBarT, DwelTime, HotBarP, ...
The analysis was done using coded units.
Estimated Regression Coefficients for Strength
Term Coef SE Coef T P
Constant 28.4429 1.664 17.094 0.000
HotBarT 3.3697 1.797 1.875 0.079
DwelTime -3.4385 1.797 -1.913 0.074
HotBarP 2.9613 1.797 1.648 0.119
MatTemp 2.1199 1.797 1.180 0.255
HotBarT*HotBarT -10.6473 3.293 -3.233 0.005
DwelTime*DwelTime -9.9043 3.293 -3.008 0.008
HotBarP*HotBarP -5.3168 3.293 -1.615 0.126
MatTemp*MatTemp -4.6029 3.293 -1.398 0.181
HotBarT*DwelTime -23.2480 4.402 -5.281 0.000
HotBarT*HotBarP -0.3480 4.402 -0.079 0.938
HotBarT*MatTemp -0.5520 4.402 -0.125 0.902
DwelTime*HotBarP 2.2000 4.402 0.500 0.624
DwelTime*MatTemp 0.9480 4.402 0.215 0.832
HotBarP*MatTemp -0.4000 4.402 -0.091 0.929
S = 4.402 R-Sq = 78.6% R-Sq(adj) = 59.8%
Analysis of Variance for Strength
Source DF Seq SS Adj SS Adj MS F P
Regression 14 1137.51 1137.514 81.2510 4.19 0.004
Linear 4 218.65 218.648 54.6619 2.82 0.060
Square 4 372.07 372.072 93.0181 4.80 0.010
Interaction 6 546.79 546.794 91.1323 4.70 0.006
Residual Error 16 310.08 310.081 19.3801
Lack-of-Fit 10 308.20 308.204 30.8204 98.51 0.000
Pure Error 6 1.88 1.877 0.3129
Total 30 1447.60
Unusual Observations for Strength
Obs StdOrder Strength Fit SE Fit Residual St Resid
17 17 20.687 14.426 3.362 6.261 2.20 R
20 20 21.375 15.100 3.362 6.275 2.21 R
21 21 25.994 20.165 3.362 5.829 2.05 R
23 23 27.428 21.720 3.362 5.708 2.01 R
R denotes an observation with a large standardized residual.
Estimated Regression Coefficients for Strength using data in uncoded units
Term Coef
Constant -289.275
HotBarT 2.28726
DwelTime 206.619
HotBarP 0.124129
MatTemp 0.593576
HotBarT*HotBarT -0.00425893
DwelTime*DwelTime -39.6171
HotBarP*HotBarP -5.31677E-04
MatTemp*MatTemp -0.00287683
HotBarT*DwelTime -0.929920
HotBarT*HotBarP -6.96000E-05
HotBarT*MatTemp -2.76000E-04
DwelTime*HotBarP 0.0440000
DwelTime*MatTemp 0.0474000
HotBarP*MatTemp -1.00000E-04
Response Surface Regression: VarStrength versus HotBarT, DwelTime, HotBarP, ...
The analysis was done using coded units.
Estimated Regression Coefficients for VarStrength
Term Coef SE Coef T P
Constant 0.91143 0.4327 2.107 0.051
HotBarT 0.54810 0.4673 1.173 0.258
DwelTime 1.04923 0.4673 2.245 0.039
HotBarP 0.04831 0.4673 0.103 0.919
MatTemp 0.60034 0.4673 1.285 0.217
HotBarT*HotBarT 1.62114 0.8562 1.893 0.077
DwelTime*DwelTime 2.34145 0.8562 2.735 0.015
HotBarP*HotBarP 1.12144 0.8562 1.310 0.209
MatTemp*MatTemp 2.27344 0.8562 2.655 0.017
HotBarT*DwelTime 5.98700 1.1447 5.230 0.000
HotBarT*HotBarP 0.69300 1.1447 0.605 0.553
HotBarT*MatTemp 0.35500 1.1447 0.310 0.760
DwelTime*HotBarP -0.18100 1.1447 -0.158 0.876
DwelTime*MatTemp -0.20300 1.1447 -0.177 0.861
HotBarP*MatTemp 1.25900 1.1447 1.100 0.288
S = 1.145 R-Sq = 76.7% R-Sq(adj) = 56.3%
Analysis of Variance for VarStrength
Source DF Seq SS Adj SS Adj MS F P
Regression 14 69.0360 69.0360 4.93114 3.76 0.007
Linear 4 10.5842 10.5842 2.64606 2.02 0.140
Square 4 20.3422 20.3422 5.08556 3.88 0.022
Interaction 6 38.1095 38.1095 6.35158 4.85 0.005
Residual Error 16 20.9651 20.9651 1.31032
Lack-of-Fit 10 20.9500 20.9500 2.09500 833.24 0.000
Pure Error 6 0.0151 0.0151 0.00251
Total 30 90.0011
Unusual Observations for VarStrength
Obs StdOrder VarStrength Fit SE Fit Residual St Resid
4 4 6.746 4.871 0.874 1.875 2.54 R
R denotes an observation with a large standardized residual.
Estimated Regression Coefficients for VarStrength using data in uncoded units
Term Coef
Constant 72.3071
HotBarT -0.425443
DwelTime -52.5837
HotBarP -0.0718131
MatTemp -0.295679
HotBarT*HotBarT 0.000648457
DwelTime*DwelTime 9.36579
HotBarP*HotBarP 0.000112144
MatTemp*MatTemp 0.00142090
HotBarT*DwelTime 0.239480
HotBarT*HotBarP 0.000138600
HotBarT*MatTemp 0.000177500
DwelTime*HotBarP -0.00362000
DwelTime*MatTemp -0.0101500
HotBarP*MatTemp 0.000314750
1.是否需要精简回归模型呢？也就是将回归项剔除，如果要剔除，应该怎样综合两个响应变量来考虑逐步剔出呢？:)
2.回归检验的方差分析中Lack-of-Fit的P值为0，代表什么意思呢，是否说明方程无效呢？:D
3.两个回归方程的RSQ都只有70%多，这代表什么意思呢，说明方程拟合不好，还是另外存在显著的因子抑或是其它原因。
HotBarT DwelTime HotBarP MatTemp Strength VarStrength
150 0.50 50 70 10.5010 4.46000
200 0.50 50 70 26.7490 0.80000
150 1.00 50 70 15.6990 0.99400
200 1.00 50 70 8.2510 6.74600
150 0.50 150 70 12.0010 2.99600
200 0.50 150 70 28.4010 0.84000
150 1.00 150 70 21.5990 2.13800
200 1.00 150 70 13.7030 4.49400
150 0.50 50 110 12.2010 4.14400
200 0.50 50 110 27.6490 1.07600
150 1.00 50 110 19.7990 2.69000
200 1.00 50 110 12.4470 5.28200
150 0.50 150 110 15.7010 3.54000
200 0.50 150 110 30.3010 3.45200
150 1.00 150 110 23.2990 2.21400
200 1.00 150 110 15.6990 6.49000
125 0.75 100 90 20.6865 1.34636
225 0.75 100 90 24.7047 1.63296
175 0.25 100 90 25.5021 1.49727
175 1.25 100 90 21.3752 2.92266
175 0.75 0 90 25.9942 0.83801
175 0.75 200 90 30.0581 1.14190
175 0.75 100 50 27.4284 1.69595
175 0.75 100 130 30.0516 2.58797
175 0.75 100 90 28.5000 0.94000
175 0.75 100 90 28.2000 0.91000
175 0.75 100 90 27.4000 0.97000
175 0.75 100 90 28.9000 0.86000
175 0.75 100 90 28.3000 0.83000
175 0.75 100 90 28.7000 0.92000
175 0.75 100 90 29.1000 0.95000
Response Surface Regression: Strength versus HotBarT, DwelTime, HotBarP, ...
The analysis was done using coded units.
Estimated Regression Coefficients for Strength
Term Coef SE Coef T P
Constant 28.4429 1.664 17.094 0.000
HotBarT 3.3697 1.797 1.875 0.079
DwelTime -3.4385 1.797 -1.913 0.074
HotBarP 2.9613 1.797 1.648 0.119
MatTemp 2.1199 1.797 1.180 0.255
HotBarT*HotBarT -10.6473 3.293 -3.233 0.005
DwelTime*DwelTime -9.9043 3.293 -3.008 0.008
HotBarP*HotBarP -5.3168 3.293 -1.615 0.126
MatTemp*MatTemp -4.6029 3.293 -1.398 0.181
HotBarT*DwelTime -23.2480 4.402 -5.281 0.000
HotBarT*HotBarP -0.3480 4.402 -0.079 0.938
HotBarT*MatTemp -0.5520 4.402 -0.125 0.902
DwelTime*HotBarP 2.2000 4.402 0.500 0.624
DwelTime*MatTemp 0.9480 4.402 0.215 0.832
HotBarP*MatTemp -0.4000 4.402 -0.091 0.929
S = 4.402 R-Sq = 78.6% R-Sq(adj) = 59.8%
Analysis of Variance for Strength
Source DF Seq SS Adj SS Adj MS F P
Regression 14 1137.51 1137.514 81.2510 4.19 0.004
Linear 4 218.65 218.648 54.6619 2.82 0.060
Square 4 372.07 372.072 93.0181 4.80 0.010
Interaction 6 546.79 546.794 91.1323 4.70 0.006
Residual Error 16 310.08 310.081 19.3801
Lack-of-Fit 10 308.20 308.204 30.8204 98.51 0.000
Pure Error 6 1.88 1.877 0.3129
Total 30 1447.60
Unusual Observations for Strength
Obs StdOrder Strength Fit SE Fit Residual St Resid
17 17 20.687 14.426 3.362 6.261 2.20 R
20 20 21.375 15.100 3.362 6.275 2.21 R
21 21 25.994 20.165 3.362 5.829 2.05 R
23 23 27.428 21.720 3.362 5.708 2.01 R
R denotes an observation with a large standardized residual.
Estimated Regression Coefficients for Strength using data in uncoded units
Term Coef
Constant -289.275
HotBarT 2.28726
DwelTime 206.619
HotBarP 0.124129
MatTemp 0.593576
HotBarT*HotBarT -0.00425893
DwelTime*DwelTime -39.6171
HotBarP*HotBarP -5.31677E-04
MatTemp*MatTemp -0.00287683
HotBarT*DwelTime -0.929920
HotBarT*HotBarP -6.96000E-05
HotBarT*MatTemp -2.76000E-04
DwelTime*HotBarP 0.0440000
DwelTime*MatTemp 0.0474000
HotBarP*MatTemp -1.00000E-04
Response Surface Regression: VarStrength versus HotBarT, DwelTime, HotBarP, ...
The analysis was done using coded units.
Estimated Regression Coefficients for VarStrength
Term Coef SE Coef T P
Constant 0.91143 0.4327 2.107 0.051
HotBarT 0.54810 0.4673 1.173 0.258
DwelTime 1.04923 0.4673 2.245 0.039
HotBarP 0.04831 0.4673 0.103 0.919
MatTemp 0.60034 0.4673 1.285 0.217
HotBarT*HotBarT 1.62114 0.8562 1.893 0.077
DwelTime*DwelTime 2.34145 0.8562 2.735 0.015
HotBarP*HotBarP 1.12144 0.8562 1.310 0.209
MatTemp*MatTemp 2.27344 0.8562 2.655 0.017
HotBarT*DwelTime 5.98700 1.1447 5.230 0.000
HotBarT*HotBarP 0.69300 1.1447 0.605 0.553
HotBarT*MatTemp 0.35500 1.1447 0.310 0.760
DwelTime*HotBarP -0.18100 1.1447 -0.158 0.876
DwelTime*MatTemp -0.20300 1.1447 -0.177 0.861
HotBarP*MatTemp 1.25900 1.1447 1.100 0.288
S = 1.145 R-Sq = 76.7% R-Sq(adj) = 56.3%
Analysis of Variance for VarStrength
Source DF Seq SS Adj SS Adj MS F P
Regression 14 69.0360 69.0360 4.93114 3.76 0.007
Linear 4 10.5842 10.5842 2.64606 2.02 0.140
Square 4 20.3422 20.3422 5.08556 3.88 0.022
Interaction 6 38.1095 38.1095 6.35158 4.85 0.005
Residual Error 16 20.9651 20.9651 1.31032
Lack-of-Fit 10 20.9500 20.9500 2.09500 833.24 0.000
Pure Error 6 0.0151 0.0151 0.00251
Total 30 90.0011
Unusual Observations for VarStrength
Obs StdOrder VarStrength Fit SE Fit Residual St Resid
4 4 6.746 4.871 0.874 1.875 2.54 R
R denotes an observation with a large standardized residual.
Estimated Regression Coefficients for VarStrength using data in uncoded units
Term Coef
Constant 72.3071
HotBarT -0.425443
DwelTime -52.5837
HotBarP -0.0718131
MatTemp -0.295679
HotBarT*HotBarT 0.000648457
DwelTime*DwelTime 9.36579
HotBarP*HotBarP 0.000112144
MatTemp*MatTemp 0.00142090
HotBarT*DwelTime 0.239480
HotBarT*HotBarP 0.000138600
HotBarT*MatTemp 0.000177500
DwelTime*HotBarP -0.00362000
DwelTime*MatTemp -0.0101500
HotBarP*MatTemp 0.000314750
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Response Surface Regression: Strength versus HotBarT, DwelTime, HotBarP, ...
The analysis was done using coded units.
Estimated Regression Coefficients for Strength
Term Coef SE Coef T P
Constant 28.443 1.467 19.387 0.000
HotBarT 3.370 1.585 2.126 0.045
DwelTime -3.438 1.585 -2.170 0.042
HotBarP 2.961 1.585 1.869 0.076
MatTemp 2.120 1.585 1.338 0.195
HotBarT*HotBarT -10.647 2.904 -3.667 0.001
DwelTime*DwelTime -9.904 2.904 -3.411 0.003
HotBarP*HotBarP -5.317 2.904 -1.831 0.081
MatTemp*MatTemp -4.603 2.904 -1.585 0.128
HotBarT*DwelTime -23.248 3.882 -5.989 0.000
S = 3.882 R-Sq = 78.1% R-Sq(adj) = 68.8%
Analysis of Variance for Strength
Source DF Seq SS Adj SS Adj MS F P
Regression 9 1131.19 1131.189 125.688 8.34 0.000
Linear 4 218.65 218.648 54.662 3.63 0.021
Square 4 372.07 372.072 93.018 6.17 0.002
Interaction 1 540.47 540.470 540.470 35.87 0.000
Residual Error 21 316.41 316.406 15.067
Lack-of-Fit 15 314.53 314.529 20.969 67.02 0.000
Pure Error 6 1.88 1.877 0.313
Total 30 1447.60
Unusual Observations for Strength
Obs StdOrder Strength Fit SE Fit Residual St Resid
3 3 20.687 14.426 2.965 6.261 2.50 R
5 5 27.428 21.720 2.965 5.708 2.28 R
9 9 25.994 20.165 2.965 5.829 2.33 R
19 19 21.375 15.100 2.965 6.275 2.50 R
R denotes an observation with a large standardized residual.
Estimated Regression Coefficients for Strength using data in uncoded units
Term Coef
Constant -289.310
HotBarT 2.25546
DwelTime 215.285
HotBarP 0.135949
MatTemp 0.570826
HotBarT*HotBarT -0.00425893
DwelTime*DwelTime -39.6171
HotBarP*HotBarP -5.31677E-04
MatTemp*MatTemp -0.00287683
HotBarT*DwelTime -0.929920
Response Surface Regression: VarStrength versus HotBarT, DwelTime, HotBarP, ...
The analysis was done using coded units.
Estimated Regression Coefficients for VarStrength
Term Coef SE Coef T P
Constant 0.91143 0.3975 2.293 0.032
HotBarT 0.54810 0.4294 1.276 0.216
DwelTime 1.04923 0.4294 2.444 0.023
HotBarP 0.04831 0.4294 0.113 0.911
MatTemp 0.60034 0.4294 1.398 0.177
HotBarT*HotBarT 1.62114 0.7867 2.061 0.052
DwelTime*DwelTime 2.34145 0.7867 2.976 0.007
HotBarP*HotBarP 1.12144 0.7867 1.425 0.169
MatTemp*MatTemp 2.27344 0.7867 2.890 0.009
HotBarT*DwelTime 5.98700 1.0518 5.692 0.000
S = 1.052 R-Sq = 74.2% R-Sq(adj) = 63.1%
Analysis of Variance for VarStrength
Source DF Seq SS Adj SS Adj MS F P
Regression 9 66.7706 66.7706 7.4190 6.71 0.000
Linear 4 10.5842 10.5842 2.6461 2.39 0.083
Square 4 20.3422 20.3422 5.0856 4.60 0.008
Interaction 1 35.8442 35.8442 35.8442 32.40 0.000
Residual Error 21 23.2304 23.2304 1.1062
Lack-of-Fit 15 23.2154 23.2154 1.5477 615.56 0.000
Pure Error 6 0.0151 0.0151 0.0025
Total 30 90.0011
Unusual Observations for VarStrength
Obs StdOrder VarStrength Fit SE Fit Residual St Resid
2 2 1.633 3.081 0.803 -1.448 -2.13 R
6 6 3.452 1.328 0.547 2.124 2.37 R
16 16 6.746 4.722 0.547 2.024 2.25 R
19 19 2.923 4.302 0.803 -1.379 -2.03 R
R denotes an observation with a large standardized residual.
Estimated Regression Coefficients for VarStrength using data in uncoded units
Term Coef
Constant 65.2099
HotBarT -0.395608
DwelTime -53.8592
HotBarP -0.0219456
MatTemp -0.240754
HotBarT*HotBarT 0.000648457
DwelTime*DwelTime 9.36579
HotBarP*HotBarP 0.000112144
MatTemp*MatTemp 0.00142090
HotBarT*DwelTime 0.239480
再看看结果：
1.R-sq值基本没有什么变化，Lack-of-Fit得P值仍然为0。
2.异常点增多，说明什么呢？
3.出现二阶项P值小于主效应项，甚至前者P值小于0.05，后者大于0.05的情况，该如何处理
4.还需要进一步处理吗？