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+ +- 根据变量的数目,可以分类一元回归、多元回归 +- 根据自变量与因变量的表现形式,分为线性和非线性 + +所以回归分析包括四个方向:一元线性回归分析、多元线性回归分析、一元非线性回归分析、多元非线性回归分析 + +![1604746129638](assets/1604746129638.png) + +> 曲线上的点,叫估计值(预测值),观测值也是真实值,观测值和估计值之间的差异叫残差。我们希望这个残差越小越好 + +回归分析的一般步骤: + +- 确认回归方程中解释变量和被解释变量 +- 确定回归模型建立回归方程 +- 对回归方程进行各种校验 +- 利用回归方程进行预测 + +#### 回归方程的定义 + +- 因变量:被预测或被解释的变量,用y表示 +- 自变量:预测或解释因变量的一个或多个变量,用x表示 +- 对于具有线性关系的两个变量,可以用一个方程来表示它们之间的线性关系 +- 描述因变量y如何以来自变量x和误差项ε的方程称为回归模型。 + +对于只涉及一个变量的一元线性回归模型可表示为: + +![1604758792278](assets/1604758792278.png) + +- y因变量 +- x自变量 +- β0表示截距 +- β1表示斜率 +- ε表示误差项,反映除x和y之间的线性关系外的随机因素对y的影响 + +如何求出β0和β1 + +一元例子: + +- 人均收入是否会影响人均食品消费支出 +- 贷款余额是否影响到不良贷款 +- 航班正点率是否对顾客投诉次数有显著影响 + +**回归方程** + +描述因变量y的期望值入喝依赖于自变量x的方程称为回归方程。根据一元线性回归模型的假设,可以得到它的回归方程为: + +![1604760128188](assets/1604760128188.png) + +- 如果回归方程中的参数已知,对于一个给定的x值,利用回归方程就能计算出y的期望值 +- 用样本统计量代替回归方程中的未知参数,就得到估计的回归方程,简称回归直线 \ No newline at end of file