【正文】 sided, or twosided H1可以是單邊或雙邊的 ? H1: bj 0 and H1: bj 0 are onesided H1: bj 0 和 H1: bj 0 是單邊的 ? H1: bj ? 0 is a twosided alternative H1: bj ? 0是雙邊替代假設(shè) ? If we want to have only a 5% probability of rejecting H0 if it is really true, then we say our significance level is 5% 如果我們愿意在 5％的概率上錯誤地拒絕實際上為真的零假設(shè)，則說我們的顯著水平為 5％ OneSided Alternatives (cont) 單邊替代假設(shè) ? Having picked a significance level, a, we look up the critical value c in a t distribution with n – k – 1 degree of freedom . 取定顯著性水平 a后，找到自由度為 n – k – 1的 t分布的臨界值 OneSided Alternatives (cont) ? If H0: bj = 0 versus H1: bj 0, we reject H0 if tbj c, fail to reject H0 if tbj =c. 如果 H0: bj = 0對 H1: bj 0，當 tbj c時我們拒絕H0，當 tbj =c，則不能拒絕 H0 ? Because t distribution is symmetric, if H0: bj = 0 versus H1: bj 0, we reject H0 if tbj c, fails to reject H0 if tbj =c. 由于 t分布是對稱的，如果 H0: bj = 0對 H1: bj 0,當 tbj c時我們拒絕 H0，當 tbj =c ，則不能拒絕 H0 yi = b0 + b1xi1 + … + bkxik + ui H0: bj = 0 H1: bj 0 c 0 a ?1 ? a? OneSided Alternatives (cont) 單邊替代假設(shè) Fail to reject reject Example: Student Performance and School Size 例子：學生表現(xiàn)與學校規(guī)模 ? Question: Does larger class size results in poorer student performance? 問題：是不是較大的班級意味著較差的學生表現(xiàn)？ ? Use 408 high schools in Michigan for year 1993, perform the following regression: 應(yīng)用 1993年 408個密歇根州中學的數(shù)據(jù)，進行如下回歸 ^math10=++ () () () –.0002enroll () math10: percentage of students passing the MEAP standardized grade 10 math test 通過 MEAP標準化 10年級數(shù)學測驗的學生百分比 totp: average annual teacher’s pensation 平均教師年度補償 staff : the number of staff per one thousand students 每千個學生對應(yīng)的工作人員數(shù)目 enroll : student enrollment 學生錄取 ? Decide the testing hypotheses: 確定被檢驗的假設(shè) ? H0 :βenroll=0 versus H1 :βenroll0 ? Compute the t statistic, 計算 t統(tǒng)計量 t=? Since nk1=404, we use the standard normal critical value. At the 5% level, the critical value is –. 由于 nk1=404，我們使用標準正態(tài)的臨界值。 CLM Assumptions 經(jīng)典線性模型假設(shè) ? Assumptions – are called the classical linear model (CLM) assumptions. 假設(shè) ? We refer to the model under these six assumptions as the classical linear model. 我們將滿足這六個假設(shè)的模型稱為經(jīng)典線性模型 ? Under CLM, OLS is not only BLUE, but also the minimum variance unbiased estimator, that is, among linear and nonlinear estimators, OLS estimator gives the smallest variance. ? 在經(jīng)典線性模型假設(shè)下， OLS不僅是 BLUE，而且是 最小方差無偏估計量 ，即在所有線性和非線性的估計量中， OLS估計量具有最小的方差。 Background Review 背景知識回顧 ? The critical value of the test statistic is the value of the statistic for which the test just reject the null hypothesis at the given s