Matlab多變量二次多項式擬合

1、X1X2X3X4X5X6X7X8Y1Y2Y3Y總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設置顯著性水平為

3、0.05，擬合得到：B=b0,b,.,1,.,b=-60.03490.02665.143017.2416151.6779對應的置信區(qū)間為：-161.405841.3359-7.587032.7488-25.570629.9709-33.50897.5362-0.3096設置顯著性水平為0.05，擬合得到：B=b0,b,.,1,.,b=-60.03490.02665.143017.2416151.6779對應的置信區(qū)間為：-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回歸效果越顯著）型不成立）。殘差圖如下12.58092.2002-12.986320.4145F=2.5616，p=0.1163，（p0.05,可知回歸模tn-歲PEAResidualCaseOrderPlotE81012CaseNumbertn-歲PEAResidualCaseOrderPlotE81012CaseNumber2L低1OE口-5-1C-15-2021416從殘差圖可以看出，除第一個數(shù)據(jù)和最后一個數(shù)據(jù)的殘差離零點均較遠，說明這兩個數(shù)據(jù)可視為異常點，去掉這兩個數(shù)據(jù)之后再做

5、擬合得到：B=b0，bb8=-478-815-71-8-85-3432824.7135-31131-9對應的置信區(qū)間為:-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,回歸效果越顯著），F(xiàn)=19.5530,p=0.0023，（p0.05,可知回歸模型成立）。殘差圖如下：ResidualCaseOrderPlot2ResidualCaseOrderPlot2469101214CaseNumberw-Enp-w8ct從殘差圖可以看出，數(shù)據(jù)的殘差離零點均較近，且殘

6、差的置信區(qū)間均包含零點，這說明回歸模型能較好的符合原始數(shù)據(jù)。預測值與實測1值的比較：Y總預測值Y總實測值相對誤差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%從上表可以看出，預測

7、值和實測值的誤差都在10%以內(nèi)，說明該擬合模型能很好的預測實驗值。最優(yōu)解：使Y總取最大值的X為：X=X,XX=1.80.90.11.59141.60.16128此時Y總的預測值為:375.7516二、對Y總做純二次多項式擬合：PureQuadraticf純二次y=4+舜呵十+隹兀+朽彳一共有17個系數(shù)，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置信區(qū)間為：-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殘差圖如下:E-rerlp-Etbct:REEidualLaEOrdePlotE81012E-rerlp-Etbct:REEidualLaEOrdePlotE8101214IEIBCaseNumber2C5O2L-預測值與實測值的比較:Y總預測值Y總實測值相對誤差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%最優(yōu)解：使Y總取最大值的X為：X=X,XX=1.8,0.3,0.1,1.5,3.0,14.0,1.6,0.16128此時Y總的預測值為:121.898三、對Y總做交互作用的二次多項式擬合：由于有8個自變量

10、，只有16數(shù)據(jù)，所以不能用交叉二項式和完全二項式。故設計一種改進的類似于交叉二項式和完全二項式的新的二項式來擬合。kitcractioii（交叉加嚴匸対+耳可+十咸耳十丫務丐互Qindrmj亡（禿全二次）工八易+爲可卄+0人+另再川內(nèi)迖1.(新的二項式)：Y二b+bX+bX+.bX+b(X+X)2+b(X+X)2+.b(X+X)2011228891210231578一共16個參數(shù)，擬合得到：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置信區(qū)間為：-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殘差圖如下:Residualu.aeyOrderPlot5D5D占B-Erlp-watld6a101214IBCasaNumber預測值與實測值的比較:Y總預測值Y總實測值相對誤差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%最優(yōu)解：使Y總取最大值的X為：X=X,XX=1.8,0.9,1.3,1.5,0.0,14.0,1.6,0.16128此時Y總的預測值為:138.0292.（另一種二項式）：Y二b+bX+bX+.bX+b(X-X)2+b(X-X)2+.b(X-X)2011228891210231578一共16個參數(shù)

14、，擬合得到：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置信區(qū)間為：-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殘差圖如下R朋idu甘IC抽9OrderPlot-102d68ID12141GCassNumbsM9O-191sCBnp-wmtr預測值與實測1值的比較：Y總預測值Y總實測值相對誤差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