数学建模——线性回归分析

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1、线性回归分析2021/8/2zhaoswallow2一、引言2004年全国数模竞赛的B题“电力市场的输电阻塞管理”第一个问题：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1~32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。2021/8/2zhaoswallow3表1各机组出力方案（单位：兆瓦，记作MW）方案机组123456780120731808012512581.1901133.02731808012512581.1

2、902129.63731808012512581.1903158.77731808012512581.1904145.32731808012512581.190512078.5961808012512581.190612075.451808012512581.190712090.4871808012512581.190812083.8481808012512581.190912073231.398012512581.1901012073198.488012512581.1901112073212.648012512581.1901212

3、073190.558012512581.190131207318075.85712512581.190141207318065.95812512581.190151207318087.25812512581.190161207318097.82412512581.190171207318080150.7112581.1902021/8/2zhaoswallow4181207318080141.5812581.190191207318080132.3712581.190201207318080156.9312581.19021120731

4、8080125138.8881.190221207318080125131.2181.190231207318080125141.7181.190241207318080125149.2981.19025120731808012512560.5829026120731808012512570.9629027120731808012512564.8549028120731808012512575.5299029120731808012512581.1104.8430120731808012512581.1111.2231120731808

5、012512581.198.09232120731808012512581.1120.442021/8/2zhaoswallow5表2各线路的潮流值（各方案与表1相对应，单位：MW）方案线路1234560164.78140.87-144.25119.09135.44157.691165.81140.13-145.14118.63135.37160.762165.51140.25-144.92118.7135.33159.983167.93138.71-146.91117.72135.41166.814166.79139.45-145.

6、92118.13135.41163.645164.94141.5-143.84118.43136.72157.226164.8141.13-144.07118.82136.02157.57165.59143.03-143.16117.24139.66156.598165.21142.28-143.49117.96137.98156.969167.43140.82-152.26129.58132.04153.610165.71140.82-147.08122.85134.21156.2311166.45140.82-149.33125.7

7、5133.28155.0912165.23140.85-145.82121.16134.75156.7713164.23140.73-144.18119.12135.57157.214163.04140.34-144.03119.31135.97156.3115165.54141.1-144.32118.84135.06158.262021/8/2zhaoswallow624167.69138.07-144.14119.19137.11157.6525162.21141.21-144.13116.03135.5154.2626163.5

8、4141-144.16117.56135.44155.9327162.7141.14-144.21116.74135.4154.8828164.06140.94-144.18118.24135.4156.6