回归模型与统计.ppt

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1、回归模型与统计软件回归模型与统计软件1引言引言2004年全国数模竞赛的B题“电力市场的输电阻塞管理”的第1个问题是这样的：某电网有8台发电机组，6条主要线路，表1和表2中的方案0给出了各机组的当前出力和各线路上对应的有功潮流值，方案132给出了围绕方案0的一些实验数据，试用这些数据确定各线路上有功潮流关于各发电机组出力的近似表达式.表表1 各机组出力方案各机组出力方案（单位：兆瓦，记作MW）方案机组123456780120731808012512581.1901133.02731808012512581.1902129.63731808012512581.1903158.77731808012

2、512581.1904145.32731808012512581.190512078.5961808012512581.190612075.451808012512581.190712090.4871808012512581.190812083.8481808012512581.190912073231.398012512581.1901012073198.488012512581.1901112073212.648012512581.1901212073190.558012512581.190131207318075.85712512581.190141207318065.958125125

3、81.190151207318087.25812512581.190161207318097.82412512581.190171207318080150.7112581.190181207318080141.5812581.190191207318080132.3712581.190201207318080156.9312581.190211207318080125138.8881.190221207318080125131.2181.190231207318080125141.7181.190241207318080125149.2981.19025120731808012512560.5

4、829026120731808012512570.9629027120731808012512564.8549028120731808012512575.5299029120731808012512581.1104.8430120731808012512581.1111.2231120731808012512581.198.09232120731808012512581.1120.44表表8.2 各线路的潮流值各线路的潮流值（各方案与表1相对应，单位：MW）方案线路1234560164.78140.87-144.25119.09135.44157.691165.81140.13-145.141

5、18.63135.37160.762165.51140.25-144.92118.7135.33159.983167.93138.71-146.91117.72135.41166.814166.79139.45-145.92118.13135.41163.645164.94141.5-143.84118.43136.72157.226164.8141.13-144.07118.82136.02157.57165.59143.03-143.16117.24139.66156.598165.21142.28-143.49117.96137.98156.969167.43140.82-152.261

6、29.58132.04153.610165.71140.82-147.08122.85134.21156.2311166.45140.82-149.33125.75133.28155.0912165.23140.85-145.82121.16134.75156.7713164.23140.73-144.18119.12135.57157.214163.04140.34-144.03119.31135.97156.3115165.54141.1-144.32118.84135.06158.2616166.88141.4-144.34118.67134.67159.2817164.07143.03

7、-140.97118.75133.75158.8318164.27142.29-142.15118.85134.27158.3719164.57141.44-143.3119134.88158.0120163.89143.61-140.25118.64133.28159.1221166.35139.29-144.2119.1136.33157.5922165.54140.14-144.19119.09135.81157.6723166.75138.95-144.17119.15136.55157.5924167.69138.07-144.14119.19137.11157.6525162.21

8、141.21-144.13116.03135.5154.2626163.54141-144.16117.56135.44155.9327162.7141.14-144.21116.74135.4154.8828164.06140.94-144.18118.24135.4156.6829164.66142.27-147.2120.21135.28157.6530164.7142.94-148.45120.68135.16157.6331164.67141.56-145.88119.68135.29157.6132164.69143.84-150.34121.34135.12157.64对函数拟合

9、，我们可以采用线性，也可以采用非线性的函数.非线性有多项式，三角函数,指数函数等，面对如本问题所示的具体数据，我们当然准备好把这些函数都拿去尝试的打算.不过那是万不得已,没招的情况下才采用的最后招数.我们做实际问题，首先想到的还是采用最简单的方法下手，如果简单的方法都可以完成得很好，当然没必要采用复杂的方法.况且对该赛题，后面还有四个更难的问题在等着我们.我们不能把第一个问题都做那么复杂吧？因此，先采用最简单的方法去尝试，是我们最可能想到的事.最简单的方法是什么？自然是采用线性的函数去表达.也就是采用线性回归分析来做！对本问题，我们采用多元线性回归分析，的确做得很好.而线性回归分析，在我们多次

10、参赛的经验来看，在许多的国内国际数学建模型竞赛中，都有可能用到.因此，下面简单介绍线性回归分析的基本原理，对回归好坏的评价指标，利用统计软件的实现。图1平面上散布点的直线拟合示意图图2SAS数据输入图图3SAS线性回归对话框表3SAS回归分析结果表TheREGProcedureModel:MODEL1DependentVariable:Y1AnalysisofVarianceSourceDFSumofSquaresMeanSquareFValuePrFModel860.735317.591915861.52|t|Intercept1110.296510.44512247.79.0001X110

11、.082840.0008465397.86.0001X210.048280.0019125.21.0001X310.052970.0006425682.44.0001X410.119930.0014980.24.0001X51-0.025440.00093315-27.26.0001X610.122010.0012696.45.0001X710.121580.0014682.99Analysis-Analyst,启动分析员.2.在弹出的表中输入数据,结果如图6图6SAS数据输入图图7SAS线性回归对话框4.SAS进行回归分析结果见下面表6TheREGProcedureModel:MODEL1D

12、ependentVariable:YAnalysisofVarianceSourceDFSumofSquaresMeanSquareFValuePrFModel42667.89944666.97486111.48|t|Intercept162.4053770.070960.890.3991x111.551100.744772.080.0708x210.510170.723790.700.5009x310.101910.754710.140.8959x41-0.144060.70905-0.200.8441表7SAS回归分析计算结果表SourceDFSumofSquaresMeanSquareFValuePrFModel4121035302595176.47|t|X112.193050.1852711.84.0001X211.153330.0479424.06.0001X310.758510.159514.760.0010X410.486320.0414111.74.0001