hapter5 How to use the multiple linear regression moce 2021/2/20
2021/2/20 1 Chapter 5 How to use the multiple linear regression model
General linear models Suppose that we have a model X=F(X1…,Xk2E) It is inherently linear for the parameters if it can be transformed into f()=A+B81(X12…,X)+…+B8(X1,…,X)+E EXamples 1.Exponential model Y=exp(B+B, X,+B,x2)e 2021/2/20
2021/2/20 2 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: 1 ( , , ; ) Y F X Xk = 0 1 1 1 1 ( ) ( , , ) ( , , ) k k k k f Y g X X g X X = + + + + 0 1 1 2 2 Y X X = + + exp( )
2. Reciprocal model Y Bo+BX+B,X,+8 3. Double-log constant elasticity)model Iny=a+BinX+& ote dyx dIny Elasticity dx y dInx B(const) 2021/2/20
2021/2/20 3 2. Reciprocal model: 3. Double-log(constant elasticity) model: 0 1 1 2 2 1 Y X X = + + + ln ln Y X = + + ln Elasticity (const.) ln dY X d Y dX Y d X = = = Note :
But the following model is not inherently linear Y=XXP +8 For others, see page72-73 2021/2/20
2021/2/20 4 But the following model is not inherently linear: For others, see page72-73 Y X X1 2 = +
a What is the dummy variable 属性因素: Man and woman City and country, developed country and developing country 经济环境的变化: Peace and war 淡季和旺季 风调雨顺和洪灾旱灾 All these have a good or bad influence on economy 2021/2/20
2021/2/20 5 ◼ What is the dummy variable 属性因素: Man and Woman, City and country, developed country and developing country 经济环境的变化: Peace and war 淡季和旺季 风调雨顺和洪灾旱灾 All these have a good or bad influence on economy