多元线性回归课件.ppt
ppxxxy2211022110 xxy22110)(xxyEp210,p,210ppxxxy22110p,210p,210y 最小niiniiipeyyQ1212210)(),()21(00000piQQiii， p,210例例4.14.1 生产总值是衡量一个国家地区经济发展的重要指标，影响一个国家或地区生产总值的因素包括资本、资源、科技、劳动力、进出口、国家基础设施建设等方面的因素。本例研究财政支出对生产总值的影响。 中国统计年鉴把财政支出划分为31个组成部分，本例只选取其中的13个重要支出项。CoefficientsCoefficientsa a-41229015612697.85-.735.473-25.70210.068-.329-2.553.02126.74217.374.2081.539.142-5.87861.983-.012-.095.926-95.66853.414-.281-1.791.091-42.28888.078-.074-.480.63711.72474.489.014.157.877-187.532273.188-.044-.686.50250.28014.018.6783.587.002-58.082187.596-.047-.310.761-81.72643.642-.302-1.873.07846.79123.185.4232.018.06054.81739.303.4491.395.18141.12314.674.2732.802.012(Constant)x1x2x3x4x5x6x7x8x9x10 x11x12x13Model1BStd. ErrorUnstandardizedCoefficientsBetaStandardizedCoefficientstSig.Dependent Variable: ya. 回归系数表用spss软件计算的回归系数如下：123456789101112134122901 25.70226.7415.87895.66842.28811.724187.53250.28058.08281.72646.79154.81741.123yxxxxxxxxxxxxx SSTSSESSTSSRyyyyRniinii112122SSTSSRRR2MSEpnSSEpnyySniiie1112) 1,() 1() 1(1212pnpFpnyypyyknSSEkSSRFniinii1xANOVAANOVAb b8.78E+016136.753E+01584.258.000a1.36E+015178.015E+0138.92E+01630RegressionResidualTotalModel1Sum ofSquaresdfMean SquareFSig.Predictors: (Constant), x13, x7, x2, x9, x6, x1, x3, x11, x5, x4, x10,x8, x12a. Dependent Variable: yb. 表中的Sig即为显著性P值，由P值0.000（近似值）可知回归方程十分显著。即可以以99.9以上的概率断言自变量所有自变量全体对因变量产生显著线性影响。对例对例4.1回归方程的检验回归方程的检验:) 1(pntStiiispnti2) 1(2xxssiei对回归系数的检验:CoefficientsCoefficientsa a-41229015612697.85-.735.473-25.70210.068-.329-2.553.02126.74217.374.2081.539.142-5.87861.983-.012-.095.926-95.66853.414-.281-1.791.091-42.28888.078-.074-.480.63711.72474.489.014.157.877-187.532273.188-.044-.686.50250.28014.018.6783.587.002-58.082187.596-.047-.310.761-81.72643.642-.302-1.873.07846.79123.185.4232.018.06054.81739.303.4491.395.18141.12314.674.2732.802.012(Constant)基本建设支出改造资金科技三项费用农业支出农林等部门事业费工交部门事业费流动部门事业费教育事业费科学事业费卫生事业费行政管理费公检法司支出城市维护费Model1BStd. ErrorUnstandardizedCoefficientsBetaStandardizedCoefficientstSig.Dependent Variable: 生产总值a. 剔除 x3科技三项费 后：CoefficientsCoefficientsa a-41548855446144.26-.763.455-25.4979.557-.326-2.668.01626.89116.821.2091.599.127-95.43851.869-.280-1.840.082-44.71281.932-.079-.546.5928.12262.282.010.130.898-179.053250.935-.042-.714.48550.47013.485.6803.743.001-60.391180.817-.049-.334.742-80.24339.609-.296-2.026.05847.02222.413.4252.098.05053.23034.567.4361.540.14140.62413.318.2703.050.007(Constant)基本建设支出改造资金农业支出农林等部门事业费工交部门事业费流动部门事业费教育事业费科学事业费卫生事业费行政管理费公检法司支出城市维护费Model1BStd. ErrorUnstandardizedCoefficientsBetaStandardizedCoefficientstSig.Dependent Variable: 生产总值a. CoefficientsCoefficientsa a-42863285211760.28-.822.421-25.1678.976-.322-2.804.01126.51816.141.2061.643.117-91.19739.346-.268-2.318.032-46.75978.306-.082-.597.557-179.366244.347-.042-.734.47250.59913.097.6823.864.001-66.501170.062-.054-.391.700-80.01038.531-.295-2.077.05245.95220.311.4152.262.03654.73831.722.4481.726.10140.14312.460.2673.222.004(Constant)基本建设支出改造资金农业支出农林等部门事业费流动部门事业费教育事业费科学事业费卫生事业费行政管理费公检法司支出城市维护费Model1BStd. ErrorUnstandardizedCoefficientsBetaStandardizedCoefficientstSig.Dependent Variable: 生产总值a. CoefficientsCoefficientsa a-37120144554130.63-.815.424-26.7787.522-.342-3.560.00228.31111.817.2202.396.026-101.27634.646-.297-2.923.00849.19411.897.6634.135.000-73.62922.303-.272-3.301.00349.94617.028.4512.933.00832.46215.730.2662.064.05145.5859.140.3034.987.000(Constant)x1x2x4x8x10 x11x12x13Model1BStd. ErrorUnstandardizedCoefficientsBetaStandardizedCoefficientstSig.Dependent Variable: ya. 用SPSS软件计算出例例4.1的增广相关阵（Correlations) 可以看出，y与x8相关系数很大，为0.971，某些自变量间相关性很高，例如r8.120.948 )(),()(221222; 1xSSExxSSExSSEry SSE(x2)是模型含有自变量x2时y的残差平方和， SSE(x1,x2)是模型中同时含有自变量x1和x2时y的残差平方和。 r2y1,2表示模型中含有x2时，y与x1的偏判定系数。C Co oe ef ff fi ic ci ie en nt ts sa a263746.6167575.01.574.126-1293.201206.739-.605-6.255.000.955-.747-.1072.580.1571.58616.383.000.990.947.279(Constant)x1x2Model1BStd. ErrorUnstandardizedCoefficientsBetaStandardizedCoefficientstSig.Zero-orderPartialPartCorrelationsDependent Variable: ya. 结结 束束
