1. 1 Econometrics

2. 2 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 ƒF „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. 3 Ch8 multiple regression 8.1 the three-variable linear regression model Y:dependent var. (or explained var.) x 2 and x 3 : independent var. (or explanatory var.) u t : the stochastic disturbance term( 不確定的誤差項， 殘差項 ， x 2, x 3 不能 100% affect Y) : intercept term( 截距項 ) 、 : partial regression coeff.

4. 4 Ch8 multiple regression 8.2 Assumption of reg. model A 8.1 Linear in parameter in Eq (8.1) => Y 與 x 2, x 3 為線性關係 A 8.2 x 2, x 3 are uncorrelated with u A 8.3 E(u i )=0 用二手資料 A 8.4 Var(u i )= => the variance of u i is constant (Homokedasticity) 變異數齊一 A 8.5 Cov(u i, u j )=0 => No autocorrelation exists between u i, u j ( 無自我相關 ) A 8.6 No exact collinear between x 2, x 3 A 8.7 for hypothesis testing,

5. 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. 6 Ch8 multiple regression Method of Ordinary Least Square (OLS) 一般最小平 方法  Choose b 1, b 2, b 3 to min where e t : : 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. 7 Ch8 multiple regression Properties of : (p.217) If A1~A4 are satisfied =>, b OLS 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 ) ƒBest: efficient =>, 用 OLS 估計 比其他方法做的還要佳, 變異數最小

8. 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 x 2 andx 3 (or regression line) jointly.

9. 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. 10 Ch8 multiple regression 8.6 Hypo. Testing ( 假設檢定 ) to test the significance of individual coeff.