三元线性回归方

三元线性回归方作者:日期:对于一个稳定生产的水泥厂家来说，其主要工艺条件，原、燃料状况，在某一较长的时间内，是基本稳定的。在此前提条件下，出厂水泥28d抗压强度与熟料3d强度、混合材掺量、水泥3d强度之间，具有线性相关关系。应用三元线性回归分析方法，可直接预报水泥28d强度。现列举工作中的一个实例，说明此预报方法的操作步骤。1设立关系式水泥28d强度y与熟料3d强度xi、混合材（煤渣）掺量X2、水泥3d强度X3之间具有直接相关关系，其回归关系式为：y=ao+aixi+a2X2+a3X3其中:ao、ai、a2、a3为回归系数。求得并验证了这些系数，就会使以后的预报来得十分方便。2选取样本选取某一段时间内的连续实际数据，剔除个别明显异常值后即为样本。一般选取30组以上的数据为好样本数据越多，回归分析结果越准确见表1。表1样本数据序号i熟料3d强度Xi混合材掺里X2水泥3d强度X3水泥28d强度y132.810.529.250.1234.011.530.651.9334.512.030.950.9434.812.031.251.4535.313.030.251.0635.013.030.149.9733.711.528.447.9831.710.528.348.5932.310.529.250.01034.111.530.150.21133.211.029.951.81233.211.029.649.51333.711.529.051.81432.111.028.849.71533.311.030.149.41633.610.530.651.61734.313.028.949.51833.912.529.351.01932.211.028.448.42033.211.027.750.02133.612.528.749.72233.612.528.350.42331.510.528.349.02433.612.527.649.22536.814.528.951.32634.612.530.251.62730.08.028.148.02833.111.029.750.72930.68.527.849.23034.712.530.150.83133.011.029.650.13232.811.027.547.93334.512.530.450.43433.412.028.649.63535.013.529.550.63633.811.530.450.53733.011.030.250.23831.69.528.249.53933.311.030.950.34033.411.029.449.74136.014.527.650.54232.410.527.848.74333.410.530.550.64435.014.030.351.14534.413.030.749.74634.613.030.449.64732.711.028.349.14833.311.527.749.24934.412.530.950.65034.412.531.452.13参数计算12 / 15n=50;m=3Lw=以/(刃J=79,125Ls=2Jx2-2-(y；xJ2=83.905几.s"?£j=61Q5朴(星nL2=力21=jXiX2一z?X二74.938,«儿>*多二 18,945l i = 1nn£23二A32-2jX3Xi一_z,n.i=1i=nnn=31,942£|J=£31=jX0Cj-.'i%li上'=1=nnn£io=-y_jXiJyi=38.769.n.«r.£20)/xajixs7t<-28.5781=1t=1i=FlRR£30-"，?工于78二37.972ih【11i-t=ILoo二E?疗一尸二55.0134求解回归系数依最小二乘法原理所得方程组aiL+azLn+U3L13=Lio，aiLi+Qz£l2+<£3£23=L加,以【Zmi+Q2L32+戊333二30及解：itnnn1VIQ|v»ai03V1qo=_jyi-一二北立上式牙7jxyn7T"n77lh几二得:ai=0.597;a2=-0.282;a3=0.397;a0=21.6805整理检验将所求得的回归系数代入(1)式即得水泥28d强度预报值为：1=21.680+0.597x1-0.282x2+0.397x3(1)检验其相关性相关系数:r二0.932r接近1,说明相关性良好。(2)检验其精度剩余标准偏差= 0.396Ly)Q1L11+2/22+以3七33)vn-m-1S值较小，说明回归方程精度良好。(3)检验其可靠性预报值?与实测值y的比较见表2,其相对误差几乎全部落于把的范围内，说明可靠性良好。表228d强度预报值与实测值的比较序号i实测y(MPa)预报r(MPa)相对误差（%150.149.9-0.4251.950.9-1.9350.951.20.6451.451.50.2551.051.10.2649.951.94.0747.949.84.0848.548.90.8950.049.6-0.81050.250.71.01151.850.3-2.91249.550.11.21351.850.1-3.31449.749.2-1.01549.450.42.01651.650.9-1.41749.550.01.01851.050.0-2.01948.449.11.42050.049.4-1.82149.749.6-0.22250.449.4-2.02349.048.8-0.42449.249.202551.351.0-0.62651.650.8-1.62748.048.51.02850.750.1-1.22949.248.6-1.23050.850.803150.150.0-0.23247.949.12.53350.450.80.83449.649.603550.650.5-0.23650.550.70.43750.250.30.23849.549.1-0.83950.350.70.84049.750.21.04150.550.0-1.04248.749.10.84350.650.80.44451.150.7-0.84549.750.72.04649.650.72.04749.149.30.44849.249.30.24950.651.00.85052.151.2-1.76结语(1)出厂水泥28d抗压强度与熟料13/153d强度、混合材掺量、水泥3d强度之间具有三元线性相关关系。(2)采用三元线性回归分析比一元或二元线性回归分析方法更能直接预报水泥28d强度。(3)采用三元线性回归分析方法预报水泥28d强度，相对误差小，可靠性fWjO(4)利用三元线性回归方程良好的可靠性、精度、相关程度，如果将混合材掺量视为因变量，则可很好地指导水泥粉磨配料。此时方程式改写为：-2L680-0.59Al0.39加3利二0.28214/15即：X2=3.546丁-2.120xi-1.408x3-76.879式中：X2需预测的混合材掺量?期望的水泥28d强度;xi已知的熟料3d强度；X3期望的水泥3d强度。15 / 15