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Econometrics

Econometrics. Ch1 The nature and scope of Econometrics Y: dependent var. => effect ( 果 ) X 1 , …X k : independent var. => cause ( 因 ) Ch2-Ch5:Review of statistic t X² F N.D Ch6-7:simple regression( 不教 ) Ch8: multiple regression ( 多元迴歸 )

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Econometrics

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  1. Econometrics

  2. Ch1 The nature and scope of Econometrics Y: dependent var. => effect (果) X1, …Xk: independent var. => cause (因) • Ch2-Ch5:Review of statistic • t • X² • F • N.D • Ch6-7:simple regression(不教) • Ch8: multiple regression (多元迴歸) * appendix 1A: (p.15) Econ data on the world wide web

  3. Ch8 multiple regression • 8.1 the three-variable linear regression model Y:dependent var. (or explained var.) x2 and x3: independent var. (or explanatory var.) ut: the stochastic disturbance term(不確定的誤差項，殘差項，x2, x3不能100% affect Y) : intercept term(截距項) 、 : partial regression coeff.

  4. Ch8 multiple regression • 8.2 Assumption of reg. model A 8.1 Linear in parameter in Eq (8.1) => Y 與x2, x3為線性關係 A 8.2 x2, x3 are uncorrelated with u A 8.3 E(ui)=0 用二手資料 A 8.4 Var(ui)= => the variance of ui is constant (Homokedasticity)變異數齊一 A 8.5 Cov(ui, uj)=0 => No autocorrelation exists between ui, uj (無自我相關) A 8.6 No exact collinear between x2, x3 A 8.7 for hypothesis testing ,

  5. Ch8 multiple regression • 8.3 estimation of parameters of multiple reg. population regression fun. (PRF): sample regression fun. (SRF): Where e: residual term = bi: the estimate of =>

  6. Ch8 multiple regression • Method of Ordinary Least Square (OLS)一般最小平方法 • Choose b1, b2, b3to min where et: : Residual sum of square (RSS) • Min RSS = F.O.C : ~ normal equation(三個方程式求三個未知數，見p.215)

  7. Ch8 multiple regression • Properties of : (p.217) If A1~A4 are satisfied => , bOLS will be BLUE (Best Linear Unbiased Estimation) • Linear: => b is a linear combination of sample observation.(線性組合) • Unbiased: E( ) = (真的 值，母體真正的 不偏) • Best: efficient => , 用OLS估計比其他方法做的還要佳,變異數最小

  8. Ch8 multiple regression • 8.4 Goodness of fit (配適度) 找出一條線最能代表觀察值 R² = multiple coeff. of determination = the proportion of the total variation in Y. :explained by x2 andx3 (or regression line) jointly.

  9. Ch8 multiple regression • TSS=ESS+RSS TSS: total sum of squares ESS: explained sum of squares RSS: residual sum of squares R²=ESS/TSS • 衡量配適度 • 用 ESS/TSS的比例來看 若RSS=0 => TSS=ESS=>R²=1 RSS ESS

  10. Ch8 multiple regression • 8.6 Hypo. Testing (假設檢定) to test the significance of individual coeff.

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