The Effect of Both the Size and The Type of Statistical Sampling on The Estimates of Simple Linear Regression Equation Coefficients
Abstract
These papers aim to study the estimation of the simple linear regression equation coefficients using the least square method at different sample sizes and different sampling methods. And so on, the main goal of this research is to try to determine the optimum size and the best sampling method for these coefficients. We used experimental data for a population consist of 2000 students from different schools all over the country. We had changed the sample size each time and calculate the coefficients and then compare these coefficients for different sample sizes with their coefficients of the real population; and the results have been shown that the estimation of the linear regression equation coefficients are close from the real values of the coefficients of the regression line equation for the population when the sample size closes the value (325). As it turns out that the Stratified random sampling with proportional distribution with class sizes gives the best and most accurate results to estimate linear regression equation with least square method.
يهدف البحث الحالي إلى دراسة تقديرات معاملات معادلة خط الانحدار الخطي البسيط باستخدام طريقة المربعات الصغرى وذلك عند حجوم عينات مختلفة وطرق معاينة مختلفة. وبذلك يكون هدف البحث هو محاولة لتحديد الحجم الأمثل والمعاينة الأفضل لتقدير هذه المعاملات. تم استخدام بيانات تجريبية لمجتمع مؤلف من 2000 فرداً من طلاب مدارس مناطق مختلفة من القطر. وقد تم في كل مرة تغيير حجم العينة وحساب المعاملات ثم مقارنة هذه المعاملات لحجوم عينات مختلفة مع معاملات المجتمع الحقيقي؛ وقد بينت النتائج أن تقديرات معاملات معادلة خط الانحدار تقترب من القيم الحقيقية لمعاملات معادلة خط الانحدار للمجتمع عندما يقترب حجم العينة من القيمة (325). كما تبين أن المعاينة بالطريقة العشوائية الطبقية ذات التوزيع المتناسب مع حجوم الفئات يعطي النتائج الأفضل والاكثر دقة لتقدير معادلة الانحدار الخطي بطريقة المربعات الصغرى.
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