Part 13- Simple linear regression - The University of Jordan

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University of Jordan Agricultural Statistic (605150)Faculty of AgricultureDr. Amer SalmanDept. of Agri. Econ. & AgribusinessY32β1= slope1β = y - Intercepto0 X1 2 3 4 5Example (13 – 1):Y = tomato productionX = fertilizer quantityY = 10 + 2xتمثل الإنتاج في حالة عدم إضافة أي كمية من السماد :10نسبة الزيادة في الإنتاج عند إضافة وحدة واحدة من السماد ‏(إنتاجية الوحدة الواحدة من السماد ( :2Yβ1= slope =2β = 10o0 X1 2 3 4 5ˆ = ˆ β + ˆ β xyo 1قيمة الإنتاج المقدرة ‏(المتوقعة ( = ŷβˆ o ,1ˆβ = estimated population parametersˆ = β + β xyo 1- 2 -
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 -
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Part 13- Simple linear regression - The University of Jordan

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