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تحلیل داده های فاصله ای در یک مدل رگرسیون خطی ساده
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در مدلهای رگرسیونی خطی ساده معمولی مقادیر متغیرهای مستقل و وابسته نقاطی تصادفی از اعداد حقیقی میباشند. در این پایاننامه یک مدل رگرسیونی خطی ساده معرفی و مورد بررسی و مطالعه قرار میگیرند. در این نوع مدل متغیرهای وابسته و مستقل دارای مقادیری از مجموعههای تصادفی با مقادیر فاصلهای حقیقی مقدار میباشند. در این تحقیق هدف بدست آوردن برآورد پارامترها و همچنین فاصلههای اطمینان برای پارامترهای این مدل میباشد. ابتدا پس از معرفی و ارائه این نوع از مدلهای رگرسیونی، مدل رگرسیونی انعطافپذیر علاقهمند به برآورد نمودن پارامترهای این مدل میباشیم. برای برآورد کردن پارامترها به یک روش تعدیل یافتهای از روش حداقل مربعات استفاده مینماییم. ویژگیهای این روش برآوردیابی را مورد مطالعه و بررسی قرار میدهیم و بر این اساس مجموعههای اطمینان برای پارامترهای این مدل ارائه میگردد. با استفاده از شبیه سازی و دادههای واقعی عملکرد این روش را مورد بررسی و مطالعه قرار میدهیم.
واژههای کلیدی : مدل رگرسیون خطی ساده، داده فاصلهای، مجموعه اطمینان، توزیع مجانبی، فاصله حسابی، برآورد حداقل مربعات.
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