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2019/12/3,1,Chapter 5 How to use the multiple linear regression model,,2,2019/12/3,,General linear models Suppose that we have a model: It is inherently linear for the parameters if it can be transformed into Examples: 1. Exponential model:,,3,2019/12/3,,2. Reciprocal model: 3. Double-log(constant elasticity) model:,4,2019/12/3,,But the following model is not inherently linear: For others, see page72-73,5,2019/12/3,,What is the dummy variable 屬性因素: Man and Woman, City and country, developed country and developing country 經(jīng)濟環(huán)境的變化: Peace and war 淡季和旺季 風調(diào)雨順和洪災旱災 All these have a good or bad influence on economy.,6,2019/12/3,,A dummy variable is a binary variable, that is, Example:,7,2019/12/3,,加法方式: 消費函數(shù) 乘法方式: 消費函數(shù) 同時考慮兩方式:,8,2019/12/3,,臨界值虛擬變量(Note: p76, 總消費函數(shù)例子是引入臨界值虛擬變量） 進口消費品額 Y, 國民收入 X 進口消費品回歸模型,9,2019/12/3,,case studies(P77-78) Use of t and F-tests to test hypotheses Involving multiple parameters Joint tests on several regression parameters: Suppose that we have a model And the null hypothesis is,,,10,2019/12/3,,The test statistic is 2. Tests involving linear functions of the regression parameters 3. Tests involving the equality of coefficients of different regression equations: Chow- test (a special F-test),11,2019/12/3,,Regression model with random explanatory variables: 1)若X與誤差項獨立, 則前面所得結論仍成立. 2)若X與誤差項不相關, 則OLSE是一致估計也是漸進無偏的. 3)若X與誤差項相關,則OLSE不是一致估計也不是漸進無偏的. OLS失效. Homework: P87, ex5.1 and 5.2,