About: Ordinary least squares

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In statistics, ordinary least squares (OLS) is a type of linear least squares method for choosing the unknown parameters in a linear regression model (with fixed level-one effects of a linear function of a set of explanatory variables) by the principle of least squares: minimizing the sum of the squares of the differences between the observed dependent variable (values of the variable being observed) in the input dataset and the output of the (linear) function of the independent variable.

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rdf:type	Thing software yago:WikicatLeastSquares yago:GeographicalArea108574314 yago:Location100027167 yago:Object100002684 yago:PhysicalEntity100001930 yago:PublicSquare108619620 yago:Region108630985 yago:YagoGeoEntity yago:YagoLegalActorGeo yago:YagoPermanentlyLocatedEntity yago:Tract108673395
rdfs:label	مربعات صغرى عادية (ar) Mínimos cuadrados ordinarios (es) Méthode des moindres carrés ordinaire (fr) 정규방정식 (ko) Ordinary least squares (en) 普通最小二乘法 (zh)
rdfs:comment	정규방정식(Normal equation 혹은 Ordinary least squares 혹은 linear least squares)은 통계학에서 선형 회귀상에서 알지 못하는 값(parameter)를 예측하기 위한 방법론이다. (ko) 在回归分析当中，最常用的估计（回归系数）的方法是普通最小二乘法（英語：ordinary least squares，簡稱OLS），它基於誤差值之上。用這種方法估计，首先要計算残差平方和（residual sum of squares；RSS），RSS是指将所有误差值的平方加起來得出的数：與的数值可以用以下算式计算出來：当中為的平均值，而為的平均值。假设总体的误差值有一个固定的變異數，這个變異數可以用以下算式估计：這個数就是均方误差（mean square error），這個分母是样本大小减去模型要估计的参数的量。這個回归模型当中有两个未知的参数（與）。而這些参数估计的标准误差（standard error）為：有了上面這个模型，研究者手上就有会有與的估计值，就可以用這個算式來预测的数值。 (zh) في الإحصاء، تشير المربعات الصغرى العادية أو المربعات الصغرى الخطية إلى طريقة تُستخدم لتقدير المعامل غير المعروف في نموذج انحدار خطي. هذه الطريقة تهدف إلى تصغير مجموع المساحات الرأسية التربيعية بين الاستجابات التي تمت ملاحظتها في مجموعة البيانات والاستجابات التي يتوقع حدوثها من التقريب الخطي. ويمكن التعبير عن نتيجة نظرية التقدير بمعادلة بسيطة، خاصةً في حالة المرتد الأحادي من الجانب الأيمن. (ar) En estadística, los mínimos cuadrados ordinarios (MCO) o mínimos cuadrados lineales es el nombre de un método para encontrar los parámetros poblacionales en un modelo de regresión lineal. Este método minimiza la suma del cuadrado de las distancias verticales entre las respuestas observadas en la muestra y las respuestas del modelo. El parámetro resultante puede expresarse a través de una fórmula sencilla, especialmente en el caso de un único regresor. (es) In statistics, ordinary least squares (OLS) is a type of linear least squares method for choosing the unknown parameters in a linear regression model (with fixed level-one effects of a linear function of a set of explanatory variables) by the principle of least squares: minimizing the sum of the squares of the differences between the observed dependent variable (values of the variable being observed) in the input dataset and the output of the (linear) function of the independent variable. (en) La méthode des moindres carrés ordinaire (MCO) est le nom technique de la régression mathématique en statistiques, et plus particulièrement de la régression linéaire. Il s'agit d'un modèle couramment utilisé en économétrie. Lorsque la matrice se décompose en , on parle de régression linéaire univariée (régression linéaire). Lorsqu'il y a plusieurs régresseurs dans la matrice , on a plutôt affaire à une régression linéaire multiple. (fr)
rdfs:seeAlso	Leverage (statistics) Simple linear regression Linear regression Quantization error model
foaf:depiction
dcterms:subject	Parametric statistics Least squares
Wikipage page ID	1651906 (xsd:integer)
Wikipage revision ID	1123558055 (xsd:integer)
Link from a Wikipage to another Wikipage	Probability distribution Proofs involving ordinary least squares Endogeneity (econometrics) Non-linear least squares Time series Projection matrix Nonnegative-definite matrix Bias of an estimator Udny Yule Variance Degrees of freedom (statistics) Design matrix Design of experiments Durbin–Watson statistic Interval estimate Null hypothesis Nuisance parameter Numerical methods for linear least squares Polynomial least squares Quantile function Convergence of random variables Correlation Parametric statistics Mathematical optimization Matrix (mathematics) Chi-squared distribution Gauss–Markov theorem Norm (mathematics) Symmetric matrix Quadratic form (statistics) Coefficient of determination Cointegration Generalized least squares Generalized method of moments Moment matrix Multivariate normal distribution Conditional expectation Consistent estimator Cross-sectional data Ergodic process Homoscedasticity Reduced chi-squared Linear equation Chow test Simple linear regression Stationary process Statistical significance Statistical unit Statistics Frisch–Waugh–Lovell theorem Idempotent matrix Identity matrix Annihilator matrix Overdetermined system P-value Statistical parameter Statistical population Observational study Total sum of squares Autocorrelation Central limit theorem

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