Part 13- Simple linear regression - The University of Jordan

University of Jordan Agricultural Statistic (605150)Faculty of AgricultureDr. Amer SalmanDept. of Agri. Econ. & AgribusinessA Test of Model UsefulnessTable (13 – 4):One tailed testH : β = 0 1Hoa: β1 < 0, or Ha: β1>Test statistic = t0ˆ β − βS ˆ β1ˆ β − βS ˆ βoTwo tailed testH : β = 0 1Hoo: β1 ≠ 01 1o o1= , to=Test statistic = t1Rejection region t < −tα, or t > tWheret αis based on (n – 2) dfαˆ β1− β1= , tS ˆ β1oˆ βo− βo=S ˆ βRejection region t < −tα/ 2, or t > tα/ 2Wheret αis based on (n – 2) dfFor example (13 – 3), we will choose α = 0.05 and, since n = 5, df = (n – 2) = 3, then therejection region for the two tailed test is:t < −t= − .182, or t > t 3.1820 .02530. 025=os2=SSEn − k=SSEn − 2Where:2SSE ( yi− yˆ ) = SSyy− ˆ β1SS∑=xy∑( y − y)2∑( ∑ yi)2SSyy=i= yi−n2 1.10s = = 0.367 ⇒ s = 0.367 = 0.613We estimated previously 1ˆβ = 0.7, s = 0.61 and SSThus:βt =s / SSxx0.7 0.7= =0.61/ 10 0.19ˆ1 =23.7xx( x )222 ∑ i (15)= ∑ xi− = 55 − = 10n5- 12 -