5-1 主主讲讲：李李宗宗璋璋 Email: Email: Lzzstat Lzzstat TEL: 189TEL: 189- -28862886- -13561356 OFFICE: OFFICE: 经经管管学学院院812812室室 华华南南农农业业学学经经管管理理学学院院会会计计系系 Functional Forms of Regression Models CHAPTER FIVE 5-2 回归模型的函数形式 nLog-linear or constant elasticity nSemilog models nReciprocal models nPolynomial regression models 5-3 B2的的含含义义 122 122 122 122 log log log log dYY levellevelYBB XuB dXX dYY dLnY YY LnYBB LnXuB dXX dLnX XX dYY dLnY YY levelLnYBB XuB dXdXX dYdYY levelYBB LnXuB dXX dLnX XX D -=+= D D -=+= D D -=+= D D -=+= D Y对对X的的边边际际效效应应 Y对对X的的弹弹性性 5-4 LIP model 5-5 5.1 How to Measure Elasticity: the Log- linear Model Log-log model:双双对对数数模模型型 Double-log model Log-linear model 2 0 02 10 12 i uB ii iii iii YB Xe LnYLnBB LnXu BLnB LnYBB LnXu = =+ = =+ Exponential regression model 5-6 Elasticity Y X dYY dY X YY E dXX dX Y XX D = D 的相 的相 对变动 对变动 Y对对X的的弹弹性性：The elasticity of Y with respect to X 12 2 = iii LnYBB LnXu dY dLnY Y BE dX dLnX X =+ = 5-7 Figure 5-1 A constant elasticity model. 5-8 Figure 5-2 5-9 Eviews Commands: equation eq5_8.ls log(y) c log(x) Eviews：log(X)对对X进进行行自自然然对对数数变变换换，取取e=2.72为为 底底的的对对数数变变换换 5-10 5.2 Compare Linear and Log-linear Regression Models If there is not strong theory, the functional form becomes an empirical question. 1.Scatter diagram works only in the two-variable regression models 2.High R-square? nLinear: the absolute change of Y nLog-linear: the relative change of Y Ex 5.16 nEven if the dependent variable in the two models is the same, R-square can always be increased by adding more explanatory variables to the model. Avoid choosing a model only on the basis of the R-square value alone! 5-11 P66, 3.5 R-Square can be computed as the squared coefficient of correlation between actual Y and the estimated Y 5-12 eq9_8.fit eq9_8_hat equ1.fit eq1_hat group g y eq1_hat eq9_8_hat g.cor 5-13 5.3 Multiple Log-linear Regression Models 多多元元双双对对数数模模型型 5-14 Cobb-Douglas Production Function () () ( ) (,) ,1 ,1 ,1 YAL K fLKALK AL K AL K AL K AL K ab ab a b ab ab ab ab l llll l lab lab lab + = = = + = += + - D 0 5-40 Hypothetical cost-output data. Equation eq5_33.Ls y c x x2 X3 5-41 Figure 5-8 Cost-output relationship. 5-42 Figure 5-9 MINITAB output of regression (9.34). 5-43 Table 5-9 Cigarette smoking and deaths from various types of cancer. 5-44 二次函数模型 2 123 23 0,Y 2 0Y iiii YBB XB Xu X dY BB X dXX =+ =+= 26.8,experwage iiiii wageBBBB Eduu dwage BB d dwage der =+ =+ =-= 增加，增加 ，增加，小减 5-51 Wage (b) logarithmic function.