مقایسهٔ روش‌ها

	خطای میانگین مربعات ریشه‌ای (RMSE)	میانگین مربعات خطا (MSE)
حوزه	ارزیابی مدل	ارزیابی مدل
خانواده	MCDM	MCDM
سال پیدایش	1809	1809
پدیدآور	Carl Friedrich Gauss	Carl Friedrich Gauss
نوع	Distance-based evaluation metric	Squared-error loss function
منبع بنیادین	Gauss, C. F. (1809). Theoria Motus Corporum Coelestium in Sectionibus Conicis Solem Ambientium. Hamburg: Perthes and Besser.	Gauss, C. F. (1809). Theoria Motus Corporum Coelestium in Sectionibus Conicis Solem Ambientium. Hamburg: Perthes and Besser.
نام‌های دیگر	RMSE, RMS error, quadratic mean error	MSE, L2 error, quadratic error
مرتبط	4	4
خلاصه	Root Mean Squared Error is a widely used metric that measures the average magnitude of prediction errors in regression models. Originating from Carl Friedrich Gauss's work on least-squares estimation (1809), RMSE quantifies how far predictions deviate from observed values by averaging the squared differences and taking the square root.	Mean Squared Error is the foundational loss function for regression models, measuring the average squared deviation between predictions and observations. Originating from Gauss and Legendre's method of least squares (1805-1809), MSE is the basis for ordinary least squares regression and remains central to modern machine learning optimization.