Part 13- Simple linear regression - The University of Jordan

University of Jordan Agricultural Statistic (605150)Faculty of AgricultureDr. Amer SalmanDept. of Agri. Econ. & Agribusinessβ∑∑x y1=2xx = X − Xy = Y − YFitting the model: the Method of Least SquaresSuppose that we have the following equation:y ˆ = −1+xx y ŷ ( y − yˆ)2( y − yˆ)(SSE)1 1 0 (1 – 0) = 1 12 1 1 (1 – 1) = 0 03 2 2 (2 – 2) = 0 04 2 3 (2 – 3) = -1 15 4 4 (4 – 4) = 0 0Sum of errors = 0 Sum of Squared errors = 2Y3y ˆ = −1+x210-11 2 3 4 5XIt can be shown that there is one (and only one) line for which the SSE is a minimum.This line is called the least square line, the regression line, the least squares equation orthe fitted line.- 3 -