Chapter3多元线性回归模型 (Muitiple linear regression model) You are required to get familiar with matrix algebra for mastering this chapter
Chapter 3 多元线性回归模型 (Multiple linear regression model) You are required to get familiar with matrix algebra for mastering this chapter!
a Classical Multiple linear regression model (CMLRM) 1. model X=b+bX1+…+ 6, X+E 2. random sample M, XI k y=b+bx1+…+b如+1(=1,…,n)
◼ Classical Multiple linear regression model (CMLRM): 1. model 2. random sample Y b b X b X 0 1 1 k k = + + + + 1 { ; , } Y X X i i ki 0 1 1 ( 1, , ) i i k ki i Y b b X b X i n = + + + + =
Matrix form Y=Xb+8 k1 8 1Ⅹ 2,b Ⅹ
Matrix form: 11 1 0 1 1 12 2 1 2 1 1 1 , , , 1 k k n n kn k n X X b Y X X b Y X X b = + = = = = Y Xb ε Y X b ε
3. Model assumption: 1.E()=0 2. E(Ge=oI,(I, is a unit matrix) 3. Xis non-random 4. rank(X)=k+l< n 5. Normality assumption E~N(0,o2)(i=1,…,n)
3. Model assumption: 1. 2. 3. is non-random. 4. 5. Normality assumption E( ) ε = 0 2 E( ) ( is a unit matrix) n n εε = I I X rank( )= 1 X k n + 2 (0, ) ( 1, , ) i N i n =
assumptions 1 and 5 imply that the errors are Independent As in the case of the univariate linear regression models, we can estimate the regression coefficients of the multiple linear regression models by using the ordinary least squares procedure. In matrix form the olse is b=(XX XY
assumptions 1 and 5 imply that the errors are Independent. As in the case of the univariate linear regression models, we can estimate the regression coefficients of the multiple linear regression models by using the ordinary least squares procedure. In matrix form, the OLSE is 1 ˆ ( − b X X) X Y =