3元线性回归方程.docVIP

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x1、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=a0+a1x1+a2x2+a3x3 ?? ?????????????????????? ?? (1)??? 其中:a0、a1、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x1混合材掺量x2水泥3d强度x3水泥28d强度y132.810.529.250.1234.011.530.651.9334.512.030.950.9434.812.031.251.4535.313.030.251.0635.013.030.149.9733.711.528.447.9831.710.528.348.5932.310.529.250.01034.111.530.150.21133.211.029.951.81233.211.029.649.51333.711.529.051.81432.111.028.849.71533.311.030.149.41633.610.530.651.61734.313.028.949.51833.912.529.351.01932.211.028.448.42033.211.027.750.02133.612.528.749.72233.612.528.350.42331.510.528.349.02433.612.527.649.22536.814.528.951.3 2634.612.530.251.62730.08.028.148.02833.111.029.750.72930.68.527.849.23034.712.530.150.83133.011.029.650.13232.811.027.547.93334.512.530.450.43433.412.028.649.63535.013.529.550.63633.811.530.450.53733.011.030.250.23831.69.528.249.53933.311.030.950.34033.411.029.449.74136.014.527.650.54232.410.527.848.74333.410.530.550.64435.014.030.351.14534.413.030.749.74634.613.030.449.64732.711.028.349.14833.311.527.749.24934.412.530.950.65034.412.531.452.1　 3? 参数计算 ???? 4? 求解回归系数??? 依最小二乘法原理所得方程组 ? ? 及解: ??? 　 ? 得:a1=0.597;a2=-0.282;a3=0.397;a0=21.680 5? 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:??? =21.680+0.597x1-0.282x2+0.397x3??? (1)检验其相关性 ???? ???? r接近1,说明相关性良好。??? (2)检验其精度??? 剩余标准偏差 ? ???? S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±5%的范围内,说明可靠性良好。 　 表2