Part 13- Simple linear regression - The University of Jordan

University of Jordan Agricultural Statistic (605150)Faculty of AgricultureDr. Amer SalmanDept. of Agri. Econ. & Agribusinessr ranges in value from -1 (for perfect negative linear correlation) to +1 (for perfectpositive linear correlation) and dose not imply causality or dependence.Example (13 – 7):The coefficient of determination for the corn – fertilizer example can be found from:R2=∑∑e2i1−2yi47.31≅ 1−= 1−0.0290 = 0.9710 ≅ 97.10%1634Thus the regression equation about 97 % of the total variation in corn output, theremaining 3 % is attributed to factors included in error term. Then:2r = R = 0.971 = 0.9854 Or 98.54 % and is positive because ˆb 1is positive.Example (13 – 8):nXiYixiX i− XyiY i− Yxiy i2xiŶi2ei( Y ) 2i− Yˆiy22Xii1 1 1 -2 -1 2 4 0.6 0.16 1 12 2 1 -1 -1 1 1 1.3 0.09 4 13 3 2 0 0 0 0 2 0 9 04 4 2 1 0 0 1 2.7 0.49 16 05 5 4 2 2 4 4 3.4 0.36 25 4n=5 ∑X =15iX =3∑ iY =2Y =10∑ ix =0ˆxiyi7β1= = 0.7 ,2x 10iˆ β ˆo= Y − β X = 2 − (0.7)(3) =Y ˆ = −0.1+ 0. 7x=∑∑2S ˆ β =S ˆ β =oo∑1−2ei×n − k n∑∑x2i2xi0.4033 = 0.6351.1= ×5 − 20.1∑ i555(10)y =0∑ =7 ∑ 2 ix i y i60.5= = 0.4033150x =10∑ 2 ie =1.1∑ 2 iX =55( Y Y ) 2i−∑ 2 iy =6- 15 -