Matlab多变量二次多项式拟合

1、X1X2X3X4X5X6X7X8Y1Y2Y3Y总0.600.50.76121.60.1619.48303685.480.60.30.91.1081.20.164.6914.792746.480.60.61.30.36140.80.124.551.443641.990.60.90.10.70100.80.127.772.413343.18100.51.56140.40.0826.322.743766.0610.31.30.30121.60.083.4910.812842.310.60.10.7681.60.043.923.842835.7610.90.51.50121.20.0416.67936

2、61.671.400.90.39100.80.163.663.523138.181.40.31.30.73140.40.165.7711.693552.461.40.60.11.59100.40.1220.554.343761.891.40.90.90.3381.60.123.853.353239.21.801.31.19121.20.08615.723758.721.80.30.11.5381.20.08301.43566.41.80.60.50.79140.80.0414.0214.383866.41.80.90.91.13100.40.043.3315.323856.65设置显著性水平为

3、0.05，拟合得到：B=b0,b,.,1,.,b=-60.03490.02665.143017.2416151.6779对应的置信区间为：-161.405841.3359-7.587032.7488-25.570629.9709-33.50897.5362-0.3096设置显著性水平为0.05，拟合得到：B=b0,b,.,1,.,b=-60.03490.02665.143017.2416151.6779对应的置信区间为：-161.405841.3359-7.587032.7488-25.570629.9709-33.50897.5362-0.309641.1386-2.59892.65200.

4、98309.3030-3.281037.7642-64.0209367.3767r2=0.7454（越接近于1回归效果越显著）型不成立）。残差图如下12.58092.2002-12.986320.4145F=2.5616，p=0.1163，（p0.05,可知回归模tn-岁PEAResidualCaseOrderPlotE81012CaseNumbertn-岁PEAResidualCaseOrderPlotE81012CaseNumber2L低1OE口-5-1C-15-2021416从残差图可以看出，除第一个数据和最后一个数据的残差离零点均较远，说明这两个数据可视为异常点，去掉这两个数据之后再做

5、拟合得到：B=b0，bb8=-478-815-71-8-85-3432824.7135-31131-9对应的置信区间为:-1048.791.17.523.9-811.6-183.512.810.575.5-1.16.7-251.4-25.8296.4-206.72470.4r2=0.9690（越接近于1,回归效果越显著），F=19.5530,p=0.0023，（p0.05,可知回归模型成立）。残差图如下：ResidualCaseOrderPlot2ResidualCaseOrderPlot2469101214CaseNumberw-Enp-w8ct从残差图可以看出，数据的残差离零点均较近，且残

6、差的置信区间均包含零点，这说明回归模型能较好的符合原始数据。预测值与实测1值的比较：Y总预测值Y总实测值相对误差42.745846.48-8.03%40.500841.99-3.55%44.935843.184.07%66.135866.060.11%42.910842.31.44%35.7635.760.00%64.450861.674.51%40.960838.187.28%52.4652.460.00%62.500861.890.99%39.275839.20.19%60.475858.722.99%64.910866.4-2.24%62.665866.4-5.62%从上表可以看出，预测

7、值和实测值的误差都在10%以内，说明该拟合模型能很好的预测实验值。最优解：使Y总取最大值的X为：X=X,XX=1.80.90.11.59141.60.16128此时Y总的预测值为:375.7516二、对Y总做纯二次多项式拟合：PureQuadraticf純二次y=4+舜呵十+隹兀+朽彳一共有17个系数，B=b,b,b,b,b=-0.2-102.32.98.1-12.601811880.315.6-48.3-109.647.5-5.9-16.216-0.1-0.5311144.8置信区间为：-5.15-34.914.4-15.416-14.416-21.619.1-1.51.6-3.86.9-2

8、4.514.9-228.7206.8-5.515-17.115.9-11.98.7-9.112.3-0.20.2-0.30.2-6.612.8-938.61167.6r2=0.9980残差图如下:E-rerlp-Etbct:REEidualLaEOrdePlotE81012E-rerlp-Etbct:REEidualLaEOrdePlotE8101214IEIBCaseNumber2C5O2L-预测值与实测值的比较:Y总预测值Y总实测值相对误差84.19185.48-1.51%47.121746.481.38%41.756241.99-0.56%44.017443.181.94%67.6019

9、66.062.33%42.894742.31.41%36.731635.762.72%60.105961.67-2.54%39.037238.182.25%51.607252.46-1.63%60.550561.89-2.16%38.385339.2-2.08%57.604758.72-1.90%66.570366.40.26%66.447766.40.07%57.156456.650.89%最优解：使Y总取最大值的X为：X=X,XX=1.8,0.3,0.1,1.5,3.0,14.0,1.6,0.16128此时Y总的预测值为:121.898三、对Y总做交互作用的二次多项式拟合：由于有8个自变量

10、，只有16数据，所以不能用交叉二项式和完全二项式。故设计一种改进的类似于交叉二项式和完全二项式的新的二项式来拟合。kitcractioii（交叉加严匸対+耳可+十咸耳十丫务丐互Qindrmj亡（禿全二次）工八易+爲可卄+0人+另再川內迖1.(新的二项式)：Y二b+bX+bX+.bX+b(X+X)2+b(X+X)2+.b(X+X)2011228891210231578一共16个参数，拟合得到：B=b,b,01b=0.0691-66.959315-100.6639-52.6693-2.06012.59696.143645.4560187.983024.42919.22445.43990.2975-

11、0.19230.2118-15.5212置信区间为：-37.291937.4301-209.335775.4172-350.2497148.9220-390.3401285.0015-179.8100175.6898-32.097237.2910-35.260247.5475-143.4469234.3590-240.8183616.7844-18.6071-83.6100-48.8672-1.3864-1.4263-2.5673-111.439867.4654102.058859.74701.98131.04172.990980.3974-18.6071-83.6100-48.8672-1.

12、3864-1.4263-2.5673-111.439867.4654102.058859.74701.98131.04172.990980.3974r2=0.9985残差图如下:Residualu.aeyOrderPlot5D5D占B-Erlp-watld6a101214IBCasaNumber预测值与实测值的比较:Y总预测值Y总实测值相对误差85.319385.48-0.19%45.905846.48-1.24%41.483641.99-1.21%43.106943.18-0.17%67.16366.061.67%41.853142.3-1.06%34.964735.76-2.22%62.9

13、32461.672.05%39.460138.183.35%51.812652.46-1.23%61.378261.89-0.83%40.464639.23.23%58.589158.72-0.22%65.903866.4-0.75%66.06166.4-0.51%56.352656.65-0.52%最优解：使Y总取最大值的X为：X=X,XX=1.8,0.9,1.3,1.5,0.0,14.0,1.6,0.16128此时Y总的预测值为:138.0292.（另一种二项式）：Y二b+bX+bX+.bX+b(X-X)2+b(X-X)2+.b(X-X)2011228891210231578一共16个参数

14、，拟合得到：B=b,b,01.,b=-1.472515-54.166339.26867.318322.9539-13.498720.6586-188.1565294.926943.2954-43.2836-0.99441.0133-0.4576-0.5168105.3503置信区间为：-224.7221.8-980.4872.1-785.1863.7-323.8338.4-216.9262.8-303.2276.2-255.2296.5-2932.92556.6-3542.24132.1-598.6685.2-609.9523.3-147.8145.8-18.320.3-13.212.3-10.79.7-1386.41597.1r2=0.9444残差图如下R朋idu甘IC抽9OrderPlot-102d68ID12141GCassNumbsM9O-191sCBnp-wmtr预测值与实测1值的比较：Y总预测值Y总实测值相对误差78.079385.48-8.66%46.577546.480.21%39.187141.99-6.68%45.166843.184.60%76.930366.0616.46%41.626142.3-1.59%37.3435.764.42