“least squares”的概念、定义、习题解题方法及翻译-数学辞典

单词

least squares

释义

least squares

The method of least squares is used to estimate parameters in statistical models such as those that occur in regression. Estimates for the parameters are obtained by minimizing the sum of the squares of the differences between the observed values and the predicted values under the model. For example, suppose that, in a case of linear regression, where Y = α + βX + ε, there are n paired observations (x1,y1), (x2,y2),…, (xn,yn). Then the method of least squares gives a and b as estimators for α and β, where a and b are chosen so as to minimize e(a,b) = ∑ (yk−a−bxk)2. Solving the simultaneous equations ∂e/∂a = 0 = ∂e/∂b gives

and $inline$ , where $inline$ and $inline$ denote the means of the xk and yk respectively.

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数学辞典收录了4151条数学词条，基本涵盖了常用数学知识及数学英语单词词组的翻译及用法，是数学学习的有利工具。