Part 13- Simple linear regression - The University of Jordan

University of Jordan Agricultural Statistic (605150)Faculty of AgricultureDr. Amer SalmanDept. of Agri. Econ. & AgribusinessYXβ = -10oβ1= -5Test of Significance of Parameter EstimatesIn order to test for statistical significance of the parameter estimates of the regressionthe variance ofbˆ o and ˆb 1is required.∑∑2var ˆx2 ibo= σu 2n xˆ 2 1varb = σu 2x∑1LiiL(1)(2)s2Sinceσ2 uis unknown, the residual variance s 2 2is used as an (unbiased) estimate ofσ u:22ˆ∑ei= σu= L(3).(Where k = number of parameter estimates).n − kUnbiased estimates of the variance ofbˆ o and ˆb 1are then given by:∑2222∑∑ ∑2 ˆ = eixi×⇒ ˆ ei(4) =−−× xiS boL S b2on k n xn k n x2∑e i= ( Y − Yˆ)n = number of observations.k = number of parameters.i∑i- 9 -