شرکت نواندیشان آماری آبیدر
آمار هیچ وقت دروغ نمی گوید، این دروغ گویان هستند که آمار می سازند.
درباره وبلاگ


نام و نام خانوادگی: ارسلان فتحی
مدرک تحصیلی: کارشناس ارشد آمار
شغل: دبیر ریاضی، پژوهشگر و تحلیل گر آماری، مدرس دانشگاه و مدیر عامل شرکت نواندیشان آماری آبیدر
میزان سابقه در تجزیه و تحلیل داده ها و مشاوره های آماری: نه سال

شماره های تماس: ۰۹۱۹۶۵۲۰۲۳۸ - ۰۹۱۸۱۷۳۴۶۰۳
پست الکترونیک: fathi.stat@gmail.com

مدیر وبلاگ : ارسلان فتحی
نویسندگان

تفاوت ضریب تعیین (R-squared) و ضریب تعیین تعدیل شده (R^2 adjusted)

تفاوت مهم میان ضریب تعیین و ضریب تعیین تعدیل شده این است که  ضریب تعیین  فرض می کند که هر متغیر مستقل  مشاهده  شده در مدل، تغییرات موجود در متغیر وابسته را تبیین می­کند. بنابراین درصد نشان داده شده توسط ضریب تعیین با فرض تأثیر همه متغیرهای مستقل بر متغیر وابسته می باشد. در صورتی که درصد نشان داده شده توسط ضریب تعییین تعدیل شده فقط حاصل از تأثیر واقعی متغیرهای مستقل مدل بر وابسته است و نه همه متغیرهای مستقل. تفاوت دیگر این است که مناسب بودن متغیرها برای مدل توسط ضریب تعیین حتی با وجود مقدار بالا قابل مشخص نیست در صورتی که می­ توان به مقدار برآورد شده ضریب تعیین تعدیل شده اعتماد کرد.

 محاسبه ضریب تعیین تعدیل شده:


 N : تعداد کل مشاهدات

 P : تعداد متغیرهای پیش­بین

R2 : ضریب تعیین

ضریب تعیین نشان می­دهد که چند درصد تغییرات متغیر وابسته به وسیله متغیر مستقل تبیین می­ شود. این ضریب در رگرسیون کاربرد زیادی دارد.

آیا معیار مناسبی برای تبیین میزان تاثیر متغیر مستقل بر متغیر وابسته است؟ - خیر - چرا؟

چون با افزایش مشاهدات و هم چنین با افزایش متغیرهای مستقل میزانافزایش می ­یابد این افزایش ممکن است کاذب باشد. برای رفع این مشکل چه کنیم؟

بهR²  تعدیل شده نیاز داریم، تعدیل شده میزانرا با توجه به متغیرهای مستقل اضافه شده به خط رگرسیون و با توجه به عرض از مبدأهای جدید، تعدیل و اصلاح می­کند. هرچه تفاوت میانوتعدیل شده کمتر باشد نشان می­دهد که متغیرهای مستقل که به مدل اضافه شده­ اند به درستی انتخاب شده­ اند.





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