1、ipipiixxxy22110多元线性回归模型、回归方程与估计的回归方程回归方程的显著性检验（线性关系的检验）非线性模型及其线性化方法令：y=lny，则有y=ln+xy1=b0+b1 x11+b2 x12+bpx1p+e1回归方程与回归系数的显著性检验3548t=0.回归系数的显著性检验（要点）回归系数的显著性检验用样本统计量 代替回归方程中的 未知参数 即得到估计的回归方程H1：bi 0 (自变量 xi 与 因变量 y有线性关系)bi 表示假定其他变量不变，当 xi 每变动一个单位时，y 的平均平均变动值22110 xxy22110)(xxyEp,210p,210p,210ppxxxy221
2、10p,210p,210y 最小niiniipeyyQ1212210)(),(),2,1(00000piQQiiip,210niiniiniiniiyyyyyyyySSTSSRR1212121221111122pnnRR修)1,(111212pnpFpnyypyypnSSEpSSRFniinii)1(pntStiiSUMMARY OUTPUTSUMMARY OUTPUT回归统计回归统计Multiple RMultiple R0.9681590250.968159025R SquareR Square0.9373318970.937331897Adjusted R SquareAdjusted
3、R Square 0.9194267250.919426725标准误差标准误差2.0100502792.010050279观测值观测值1010方差分析方差分析dfdfSSSSMSMSF FSignificance FSignificance F回归分析回归分析2 2 423.01789423.01789 211.50894211.50894 52.3497852.349786.1612E-056.1612E-05残差残差7 7 28.28211528.282115 4.04030214.0403021总计总计9 9451.3451.3CoefficientsCoefficients 标准误差标
4、准误差t Statt StatP-valueP-valueLower 95%Lower 95%Upper 95%Upper 95%InterceptIntercept-38.8251694-38.8251694 8.47859118.4785911-4.579201-4.579201 0.0025460.002546-58.873837-58.873837-18.7765-18.7765X Variable 1X Variable 11.3406936181.340693618 0.14331590.1433159 9.35481479.3548147 3.31E-053.31E-051.001805621.001805621.6795821.679582X Variable 2X Variable 20.0228022930.022802293 0.00475420.0047542 4.79621724.7962172 0.0019750.0019750.011560350.011560350.0340440.03404411)1(122pnnRR调整1)(12pnyySniiy210228.0341.18252.38xxy一个含有四个变量的回归xeyxy xxyxylgxey104812160200040006000生产率生产率废废品品率率结结 束束
