1.2可线性化的回归分析学案 | 备注 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
【学习目标】 1. 能直观的判断两个变量是否满足线性相关 2. 用非线性的函数关系来描述不好用线性关系刻画的两个变量之间的关系 【重点、难点】用非线性的函数关系来描述不好用线性关系刻画的两个变量之间的关系 【自主学习】 1.若两个变量不呈现线性关系，不能直接利用线性回归方程建立两个变量的相关关系，那我们应如何建立两个变量的关系？例如 2. 在具体问题中，我们首先应该作出原始数据 3. 对于非线性回归模型一般可转化为 模型从而得到相应的回归方程。 4.几种能转化为线性回归模型的非线性回归模型 （1）幂函数曲线 （2）指数曲线 （3）倒指数曲线 （4）对数曲线 【例题分析】 例1.（1）有5组（x,y）数据(1,3),(2,4),(4,5),(3,10),(10,12)，去掉一组______数据后，剩下的四组数据的线性相关系数最大。 （2）已知幂函数曲线 例2.为了研究某种细菌随时间x变化，繁殖的个数，收集数据如下：
（1）用天数作解释变量，繁殖个数作预报变量，作出这些数据的散点图； （2）试求出预报变量对解释变量的回归方程.（答案：所求非线性回归方程为 小结：利用回归方程探究非线性回归问题，可按“作散点图 其关键在于如何通过适当的变换，将非线性回归问题转化成线性回归问题. 【课后巩固】 1． A. C. 2．为考虑广告费用x与销售额y之间的关系，随机地抽取5家超市，得到如下表所示的数据；
现要使销售额达到10万元，则广告费用约为______________千克. 3. 已知两个变量x，y的关系可以近似的用函数 4. 在彩色显影中，由经验可知，形成染料光学密度y与析出银的光学密度x由公式 现测得试验数据如下：
试求y对x的回归方程. 5.在一次抽样调查中测得样本的5个样本点，数值如下表：
试建立y与x之间的回归方程． | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
课后反思： | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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