统计学 课件 第20讲 一元线性回归的参数估计.pptx

第20讲一元线性回归的参数估计课程类别：专业必修课授课对象：经管类本科生1

引例：地下停车位的市场价格?相关因素1.根据成本确定销售价格2.根据市场价格确定销售价格……2

引例：地下停车位的市场价格调研周边的其他楼盘编号车位价格（万元）编号车位价格（万元）A011.2188.6A151.56316.2A021.09310.3A161.80415.4A031.0417.5A171.85315.3A041.29310.3A181.0917A051.3659.45A191.0637.1A061.66216.4A201.63515.1A071.5213.2A211.2529.4A082.65921.2A221.088.2A091.50512.2A231.3058.6A101.52512A241.22110.2A112.04818.6A250.9347.3A121.88313.8A261.85318.5A132.71224.1A271.2539.2A142.07215.4A280.8848.63

一元线性回归Stanton,J.M.(2001).Galton,Pearson,andthepeas:Abriefhistoryoflinearregressionforstatisticsinstructors.?JournalofStatisticsEducation,?9(3).FrancisGalton(1822?–1911)4?由于x的变化而引起的y的变化其它随机因素对y的影响?

一元线性回归基本假定线性关系x的非随机性ε是同方差的（σ2是常数）E(ε)=0ε~N(0,σ2)ε相互独立?截距斜率（回归系数）x=x2时的E(y2)x=x1时y的分布x2x1x=x1时的E(y1)?xyx=x2时y的分布?5

参数的最小二乘估计在二维空间中，这样的直线似乎是无穷多的，我们能不能找到最好的？?总体回归参数：未知样本?样本统计量代替未知参数得到估计的回归方程6

参数的最小二乘估计xy(xn,yn)(x1,y1)(x2,y2)(xi,yi)????7

参数的最小二乘估计思想：因变量的观察值与估计值之间的误差平方和达到最小.CarlFriedrichGauss(1777–1855)??最小二乘估计（LeastSquaresEstimation）最小二乘估计8

参数的最小二乘估计????9

例题?10编号车位价格（万元）编号车位价格（万元）A011.2188.6A151.56316.2A021.09310.3A161.80415.4A031.0417.5A171.85315.3A041.29310.3A181.0917A051.3659.45A191.0637.1A061.66216.4A201.63515.1A071.5213.2A211.2529.4A082.65921.2A221.088.2A091.50512.2A231.3058.6A101.52512A241.22110.2A112.04818.6A250.9347.3A121.88313.8A261.85318.5A132.71224.1A271.2539.2A142.07215.4A280.8848.6

例题?编号A011.2188.610.4751.484A021.09310.311.2581.195A031.0417.57.8081.084A041.29310.313.3181.672A051.3659.4512.8991.863A061.66216.427.2572.762A071.5213.220.0642.310A082.65921.256.3717.070A091.50512.218.3612.265A101.5251218.3002.326A112.04818.638.0934.194A121.88313.825.9853.546A132.71224.165.3597.355A142.07215.431.9094.293A151.56316.225.3212.443A161.80415.427.7823.254A171.85315.328.3513.434A181.09177.6371.190A191.0637.17.5471.130A201.63515.124.6892.673A211.2529.411.7691.568A221.088.28.8561.166A231.3058.611.2231.703A241.22110.212.4541.491A250.9347.36.8180.872A261.85318.534.2813.434A271.2539.211.52