【正文】 ept as simple as possible until proved inadequate would suggest that we keep our regression model as simple as possible.“奧卡姆剃刀原則”，描述應(yīng)該盡可能簡(jiǎn)單，只要不遺漏重要信息。 In linear regression analysis our primary objective is to explain the behavior of the dependent variable in relation to the behavior of one or more other variables, allowing for the data that the relationship between them is （應(yīng)變量）與其他一個(gè)或多個(gè)變量（自變量）只見(jiàn)的行為關(guān)系，當(dāng)然這種關(guān)系并非完全正確l Step5：估計(jì)經(jīng)濟(jì)計(jì)量模型參數(shù)216。 Three types of data三類可用于分析的數(shù)據(jù)1) Time series(時(shí)間序列數(shù)據(jù)):Collected over a period of time, are collected at regular 2) Crosssectional截面數(shù)據(jù):Collected over a period of time, are collected at regular 3) Pooled data合并數(shù)據(jù)（上兩種的結(jié)合）l Step3：設(shè)定數(shù)學(xué)模型1. plot scatter diagram or scattergram2. write the mathematical modell Step4：設(shè)立統(tǒng)計(jì)或經(jīng)濟(jì)計(jì)量模型216。 CLFPR is dependent variable應(yīng)變量216。 In short, the estimated regression line gives the relationship between average CLFPR and CUNR 簡(jiǎn)言之，估計(jì)的回歸直線給出了平均應(yīng)變量和自變量之間的關(guān)系216。這表明回歸模型應(yīng)盡可能簡(jiǎn)單。2) Assumption 2: The explanatory variables X is uncorrelated with the disturbance term U. X’s are nonstochastic, U is stochastic. 解釋變量X與擾動(dòng)誤差項(xiàng)u不相關(guān). X是非隨機(jī)的，U是隨機(jī)的。l Homoscedasticity（同方差）:a. This assumption simply means that the conditional distribution of each Y population corresponding to the given value of X has the same variance. 該假定表明，與給定的X相對(duì)應(yīng)的每個(gè)Y的條件分布具有同方差。There is no specification bias or specification error in the 。 theorem 高斯馬爾科夫定理Given the assumptions of the classical linear regression model (CLRM), the OLS estimators have minimum variance in the class of linear OLS estimators are BLUE (best linear unbiased estimators)滿足古典線性模型的基本假定，則在所有線性據(jù)計(jì)量中，OLS估計(jì)兩具有最小方差性，即OLS是最優(yōu)線性無(wú)偏估計(jì)量（BLUE）10. BLUE property 最優(yōu)線性無(wú)偏估計(jì)量的性質(zhì)1) B1 and B2 are linear estimators. B1和B2是線性估計(jì)量2) They are unbiased , that is E(b1)=B1, E(b2)=B2. B1和B2是無(wú)偏估計(jì)兩3) The OLS estimator of the error variance is 4) b1 and b2 are efficient Var(b1) is less than the variance of any other linear unbiased estimator of B1Var(b2) is less than the variance of any other linear unbiased estimator of B211. Monte Carlo simulation 蒙特卡洛模擬l Do the experiment at labl Do it by Excell. =NORMINV(RAND(),0,2)l Do it by matlab.= NORMINV(uniform(),MU,SIGMA)l Do it by Stata. =invnorm(uniform())12. Central Limit Theorem’s 中心極限定理If there is a large number of independent and identically distributed (iid) random variables, then, with a few exceptions , the distribution of their sum tends to be a normal distribution as the number of such variables increases indefinitely. 隨著變量個(gè)數(shù)的無(wú)限增加，獨(dú)立同分布隨機(jī)變量近似服從正態(tài)分布13. RecallU, the error term represents the influence of all those forces that affect Y but are not specifically included in the regression model because there are so many of them and the individual effect of any one such force on Y may be too minor. 誤差項(xiàng)代表了未納入回歸模型的其他所有因素的影響。17. We need some formal testing procedure to reject or receive the null hypothesis and make the skeptical guys shut 18. If our null hypothesis is B2=0 and the puted b2=, we can find out the probability of obtaining such a value from the Z, the standard normal =0，計(jì)算得到b2=，那么根據(jù)標(biāo)準(zhǔn)正態(tài)分布Z，能夠求得獲此b2值的概率If the probability is very small, we can reject the null ，則拒絕零假設(shè)。b. in repeated applications 95 out of 100 such intervals will include the true B2重復(fù)上述過(guò)程，100個(gè)這樣的區(qū)間中將有95個(gè)包括真實(shí)的B2。26. A cautionary noteAlthough the statement given is true, we cannot say that the probability is 95 percent that the particular interval includes B2, for this interval is not a random interval, it is fixed, therefore, the probability is either 1 ore 0 that the interval includes ，%，而不是一根隨機(jī)區(qū)間， can only say that if we construct 100 intervals like this interval, 95 out of 100 such intervals will include the true ， can not guarantee that this particular interval will necessarily includes .27. The test of significance approach to hypothesis testing 假設(shè)檢驗(yàn)的顯著性檢驗(yàn)方法Hypothesis testing is that of a test statistic and the sampling distribution of the test statistic under the null hypothesis, 。30. ConclusionsIn the case of twosided t test 雙邊檢驗(yàn)情況中If the puted |t|, the absolute value of t, exceeds the critical t value at the chosen level of significance, we can reject the null |t|值超過(guò)臨界t值，則拒絕零假設(shè)。32. How can we puted tWe first pute the t value as if the null hypothesis were that B2=0, we still get the t首先計(jì)算在零假設(shè)B2=0下的t值Since this value exceeds any of the critical values shown in the preceding table, following the rules laid down. t值大與上表給出的任何臨界值，附錄D表D2列出的規(guī)則，We can reject the hypothesis that annual family ine has no relationship to math . ：家庭年收入對(duì)數(shù)學(xué)SAT沒(méi)有影響。41. ESS vs RSSa. If the chosen SRF fits the data quite well, ESS should be much larger than ，則SEE遠(yuǎn)大于RSS。An R2 of 1 means a “perfect fit” for the entire variation in Y is explained by the =1，則表示完全擬合，即線性模型完全解釋Y的變異。48. P valueBy quoting the P values we can determine the exact level of significance of the estimated t value. 通過(guò)列出的p值能夠確定t值的精確顯著水平。If it is greater than the critical P value the null hypothesis may not be ，則不能拒絕原假設(shè)。第四章 Why should we introduce multiple regression model ?為什么介紹多元回歸模型Because multiple influences (., variable) may affect the dependent variable. The Threevariable regression model三變量線性回歸模型1　 The threevariable PRF to its nonstochastic form：三變量PRF的非隨機(jī)形式
： The conditional mean value of Yt, conditional upon the given or fixed values of the variables X2 and X3給定XX3取值下Y的條件均值We obtain the average or mean value of Y for the fixed values of X variables.給定解釋變量X取值條件下，得到的Y的均值2　 The threevariable PRF to its stochastic form三變量PRF的隨機(jī)形式 Any individual Y value can be expressed as the sum of two ponents
Any individual Y value can be expressed as the sum of two ponents：任何一個(gè)Y值可以表示成兩部分之和l a systematic or deterministic，ponents ，Which is simply its mean value系統(tǒng)成分或確定性成分也就是Y的均值 l Ut , which is the nonsystematic or random ponent determined by factors other than X2 and Ut ，由除X2,X3以外的因素決定。A ex