Part 13- Simple linear regression - The University of Jordan

University of Jordan Agricultural Statistic (605150)Faculty of AgricultureDr. Amer SalmanDept. of Agri. Econ. & Agribusiness∑22ei1∑×⇒ ˆei(5) S b =− ∑−×21n k xin k ∑2 bˆ1= 12xiS LSo that S b ˆ o and S ˆb 1are the standard errors of the estimates. SinceU iis normallydistributed, Yiand therefore bˆ o and ˆb 1are also normally distributed, so that we can use thet distribution with n – k degrees of freedom, to test hypotheses about and constantconfidence intervals forbˆ o and ˆb 1.tocalbo− bo= ˆSbo,t1calbˆ1− b=Sb11df = n – k (n – 2 always).α = 5 %; one tailed (α), two tailed (α/2).Example (13 – 6):The following table shows the calculations required to test the statistical significanceofbˆ o and ˆb 1. The value of Yˆ iin the table are obtained by subtracting the values of Xiintothe estimated regression equation Yˆ 2i= 27.12 + 1. 66Xi(The values of yiare obtained bysquaring yi( Y i− Y ).Table (13 – 3):year Y (corn)iXi(fertilizer)Yˆ i( Y − Yˆ)e= i2ei2Xi2xi2yi2( Y i− Y )1 40 6 37.08 2.92 8.5264 36 144 2892 44 10 43.72 0.28 0.0784 100 64 1693 46 12 47.04 -1.04 1.0816 144 36 1214 48 14 50.36 -2.36 5.5696 196 16 815 52 16 53.68 -1.68 2.8224 256 4 256 58 18 57.00 1.00 1.0000 324 0 17 60 22 63.64 -3.64 13.2496 384 16 98 68 24 66.96 1.04 1.0816 576 36 1219 74 26 70.28 3.72 13.8384 676 64 28910 80 32 80.24 -0.24 0.0576 1,024 196 529n=10∑Y i=570Y =57∑ iX =180X =18∑ ie =0∑e2 i=47.3056∑ X2i=3,816∑ x2 i=576∑ y2 i=1,634- 10 -