Ordinary least squares是什么意思?
In?statistics,?ordinary least squares?(OLS) or?linear least squares?is a method for estimating the unknown parameters in a?linear regression model, with the goal of minimizing the sum of the squares of the differences between the observed?responses?(values of the variable being predicted) in the given?dataset?and those predicted by a linear function of a set of?explanatory variables. Visually this is seen as the sum of the squared vertical distances between each data point in the set and the corresponding point on the regression line – the smaller the differences, the better the model fits the data. The resulting?estimator?can be expressed by a simple formula, especially in the case of a?single regressor?on the right-hand side.
The OLS estimator is?consistent?when the regressors are?exogenous, and?optimal in the class of linear unbiased estimators?when the?errors?are?homoscedastic?and?serially uncorrelated. Under these conditions, the method of OLS provides?minimum-variance mean-unbiased?estimation when the errors have finite?variances. Under the additional assumption that the errors are?normally distributed, OLS is the?maximum likelihood estimator.
OLS is used in fields as diverse as?economics?(econometrics),?political science,?psychology?and?electrical engineering?(control theory?and?signal processing).
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