高中数学-第三章-统计案例-31-回归分析-311-回归分课件.ppt

1、第三章 统计案例1 1回归分析回归分析1 1.1 1回归分析目标导航知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练目标导航目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识

2、梳理1.通过实例掌握回归分析的基本思想方法.2.利用最小二乘法会求线性回归直线方程,并能用线性回归直线方程进行预报.目标导航知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练目标导航目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUI

3、TANGYANLIAN随堂演练ZHISHISHULI知识梳理121.线性回归方程假设样本点为(x1,y1),(x2,y2),(xn,yn),设线性回归直线方程为y=a+bx,要使这n个点与直线y=a+bx的“距离”平方之和最小,即使得Q(a,b)=(y1-a-bx1)2+(y2-a-bx2)2+(yn-a-bxn)2达到最小,a,b需满足对两个变量之间的相关关系进行统计分析的方法叫回归分析.回归分析是寻找相关关系中非确定性关系的某种确定性.如果散点图中样本点的分布从整体上看大致在一条直线附近,我们称这两个变量之间具有线性相关关系,这条直线叫线性回归直线,从整体上看各点与此直线的距离平方之和最小

4、,即该直线最贴近已知的样本点,最能代表变量x与y之间的关系.目标导航知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练目标导航目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识

5、梳理122.求线性回归方程的一般步骤(1)作出散点图,将问题所给的数据在平面直角坐标系中描点,这样表示出的具有相关关系的两个变量的一组数据的图形就是散点图.从散点图中我们可以看出样本是否呈现条状分布,从而判断两个变量是否具有线性相关关系.(2)求回归系数a,b,其具体步骤为:将所给的数据xi,yi列成相应的表格,如下表所示:目标导航知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练目标导航目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SU

6、ITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理12目标导航知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练目标导航目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHUL

7、I知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理12【做一做1】随机抽样中得到四个样本点分别为(1,2),(2,3),(3,4),(4,5),则y与x之间的回归直线方程为()A.y=x+1B.y=x+2C.y=2x+1D.y=x-1答案:A目标导航知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练目标导航目标导航DIANLITOUXI典例透析SUITANGYANLI

8、AN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理12【做一做2】某设备的使用年限x(单位:年)和所支出的维修费用y(单位:万元)有如下的统计资料:若由资料知,y与x呈线性相关关系.试求:(1)线性回归方程y=bx+a的回归系数a,b;(2)估计使用年限为10年时,维修费用是多少?目标导航知识梳

9、理典例透析随堂演练目标导航知识梳理典例透析随堂演练知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练目标导航目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理12目标导航知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练知

10、识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练目标导航目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理题型一题型二【例1】在关于人体的脂肪含量(百分比)和年龄关系的研究中,研究人员获得了一组数据:(1)假设x与y之间呈现近似

11、的线性相关关系,求y与x之间的线性回归方程;(2)给出37岁人的脂肪含量的预测值.目标导航知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练目标导航目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZH

12、ISHISHULI知识梳理题型一题型二分析:两个变量呈现近似的线性相关关系,可通过公式计算出其线性回归方程,并根据方程求出预测值.解:(1)设线性回归方程为y=a+bx,根据已知列表如下:目标导航知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练目标导航目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练Z

13、HISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理题型一题型二目标导航知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练目标导航目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIAN

14、LITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理题型一题型二反思本题关键在于利用公式求b和a,确定线性回归方程.目标导航知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练目标导航目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航

15、DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理题型一题型二【变式训练1】某5名学生的数学和化学成绩如下表:(1)画出散点图;(2)求化学成绩y对数学成绩x的线性回归方程.目标导航知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练目标导航目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUI

16、TANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理题型一题型二目标导航知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练目标导航目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHIS

17、HULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理题型一题型二【例2】某农场对单位面积化肥用量x(单位:kg)和水稻相应产量y(单位:kg)的关系作了统计,得到数据如下:求出线性回归方程,并预测当单位面积化肥用量为32 kg时,水稻的产量大约是多少?(精确到0.01 kg)目标导航知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练目标导航目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITO

18、UXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理题型一题型二目标导航知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练目标导航目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随

19、堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理题型一题型二目标导航知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练目标导航目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航

20、DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理题型一题型二【变式训练2】某地最近十年粮食需求量逐年上升,下表是部分统计数据:(1)利用所给数据求年需求量与年份之间的回归直线方程y=bx+a;(2)利用(1)中所求出的直线方程预测该地2016年的粮食需求量.目标导航知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练目标导航目标导航DIANLITOUXI典例透析SUITANGYANLI

21、AN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理题型一题型二目标导航知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练目标导航目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目

22、标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理123451.对具有线性相关关系的两个变量建立的线性回归方程y=a+bx中,回归系数b()A.可以小于0B.只能大于0C.可能等于0D.只能小于0解析:b可能大于0,也可能小于0,但当b=0时,x,y不具有线性相关关系.答案:A目标导航知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演

23、练知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练目标导航目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理123452.下列两个变量间的关系不是函数关系的是()A.正方体的棱长与体积B.角的弧度数与它的正弦值C.单产为常数时

24、,土地面积与粮食总产量D.日照时间与水稻亩产量答案:D目标导航知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练目标导航目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理1

25、23453.已知两个变量x和y之间具有线性相关性,甲、乙两个同学各自独立地做了10次和15次试验,并且利用线性回归的方法求得回归直线分别为l1和l2,已知两个人在试验中发现对变量x的观测数据的平均数都为s,对变量y的观测数据的平均数都是t,则下列说法正确的是()A.l1与l2一定有公共点(s,t)B.l1与l2相交,但交点一定不是(s,t)C.l1与l2必定平行D.l1与l2必定重合答案:A目标导航知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练目标导航目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZH

26、ISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理123454.某城市供电局为了了解用电量y(单位:度)与气温x(单位:)之间的关系,随机统计了某4天的用电量与当天气温,并制作了对照表:由表中数据,得线性回归方程y=-2x+a,当气温为-4 时,预测用电量的度数约为.目标导航知识梳理典例透析随堂演练目标导航知识

27、梳理典例透析随堂演练知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练目标导航目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理123455.某工厂18月份某种产品的产量x与成本y的统计数据见下表:(1)画出散点图.(2)y与x

28、是否具有线性相关关系?若有,求出其线性回归方程.目标导航知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练目标导航目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理12345目标导航知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练目标导航目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理12345