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1、【课题】10.5 一元线性回归【教学目标】知识目标：(1)了解相关关系的概念(2)掌握一元线性回归思想及回归方程的建立能力目标：增强学生的数据处理能力，计算工具的使用能力，分析问题和解决问题的能力，培养严谨、细致的学习和工作作风【教学重点】掌握一元回归方程【教学难点】理解相关关系、回归分析概念【教学设计】一切自然现象和社会现象都不是孤立的事物与事物之间，变量与变量之间，都存在着某种关系这类关系大体可分为两类：一类是确定性的，另一类是非确定性的用来近似地描述具有统计相关关系的变量之间关系的函数叫做回归函数一元回归处理两个变量之间的相关关系问题如果两个变量之间的相关关系是线性的，就是一元线性回归问
2、题本教材根据学生的实际情况只介绍两个变量间的一元线性回归问题通过建立回归方程，可以对相应的变量进行预测和控制回归分析具有广泛的应用在本节教学过程中，由于统计量的计算十分繁杂，因此，必须注重训练学生利用计算器或计算机软件进行计算、求解的能力【教学备品】教学课件【课时安排】2 课时(90 分钟)【教学过程】教学过程教师行为学生行为教学意图时间*揭示课题10.5 一元线性回归介绍了解0 教学过程教师行为学生行为教学意图时间*创设情境兴趣导入【问题】人的身高（cm）与体重(kg)之间有没有联系呢?也许有人知道，平均标准体重的数值约为体重身高-105这个结果是通过大量样本的分析，估算出来的质疑讲解说明思
3、考启发学 生思考5*动脑思考探索新知【新知识】表 1012 中是随机抽取的8 个学生的身高(单位:cm)与体重(单位:kg)的数据:表 1012编号1 2 3 4 5 6 7 8 身高 x172 150 170 165 180 176 155 160 体重 y60 47 85 70 75 80 50 65 学生的身高与体重之间存在着一定的关系，这种关系不像以前研究的函数关系那样，知道身高，就能确定体重的值但是一般身高的人，体重还是比较大的变量之间的这种非确定性的相互依存的关系叫做相关关系它的特点是，当一个变量或n 个变量的值确定后，另一个变量的值虽然与它（或它们）有着密切的关系，但却无法完全确
4、定下面要研究的问题是，能否利用确定性的关系来近似的描述相关关系讲解说明引领分析理解记忆带领学生分析15*运用知识强化练习请举出具有相关关系变量的实例提问回答20*动脑思考探索新知【新知识】我们继续研究8 个学生的身高与体重的关系建立平面直角坐标系oxy，x 轴表示身高(单位:cm)，y轴表示体重(单位:kg).上述样本中每位学生的身高与体重组成的有序数对(,)x y，对应于平面上一个点，这些点组成的图形叫做 散点图.如图 10 8 所示.讲解说明思考文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 Z
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10、O5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4
11、S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1教学过程教师行为学生行为教学意图时间图 10-8表面上散点图中的这些点杂乱无章，但是大体上呈现出一种直线走向趋势这是非常重要的，否则不能用一次函数来近似.这启发我们，人的体重 y 与身高 x 大体上有一次函数的关系，即可以近似地有yabx(10.5)其中 a、b 是未知的，可以用样本的数据去估计a、b 的值，估计
12、值分别写作a?和b?一般地，用1122(,),(,),(,)nnx yxyxy表示数据的n 个有序实数对，则可证明得到a?与b?的计算公式如下：1112211()()?,()nnniiiiiiinniiiinx yxybnxx?,aybx其中1111,nniiiixx yynn方程?yabx（10.6）叫做 y 关于 x 的回归方程，它的图形叫做回归直线.【说明】引领分析仔细分析关键语句讲解说明理解记忆观察带领学生分析启发学生思考文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L
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18、 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6
19、O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1教学过程教师行为学生行为教学意图时间是求和符号,121ninixxxx【计算器使用】可以利用计算器来求出a?和b?，具体步骤如下：1设置统计计算状态（STAT）操作：按一次MODE，会显示1:COMP2:STAT3:TABLE，表示进入计算状态选项，按2 进入统计计算模块2输入数据操作：在上一步的基础上，按键2 进入线性回归计算（A
20、+Bx）指令，依次输入数值，即172=150=170=165=180=176=155=160=，然后用中间光标键把输入位置移到Y 下的第一位置，依次输入的数值，即60=47=85=70=75=80=50=65 AC 在输入中注意x 的量和 y 的量要对应起来3显示计算结果（1）按键SHIFT1，然后按键5，最后依次按键1=，显示回归系数：105A（2）按键SHIFT1，然后按键5，最后依次按键2=，显示回归系数：1.02B因此，身高与体重之间的关系的线性回归方程为1.02105yx即体重身高-105【软件链接】利用 Excel 软件可以求出回归曲线和回归方程其步骤为：（1）在 Excel 工作
21、表中输入数据(如图 109)引领分析仔细分析关键语句思考理解记忆带领学生思考文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5
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26、6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10
27、L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1教学过程教师行为学生行为教学意图时间图 109（2）选中数据区，按菜单栏的“插入图表图表类型
28、散点图完成”得出散点图（如图 1010）图 1010 讲解说明引领分析观察思考理解记忆启发学生思考文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L
29、1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:
30、CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G
31、10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3
32、 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8
33、I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2
34、 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1教学过程教师行为学生行为教学意图时间（3）选中图表，按菜单栏的“图表添
35、加趋势线”，然后在“类型”中选“线性”，在“选项”中选定“显示公式”，“确定”如图 1011，图表中显示模拟直线以及回归方程图 1011【说明】由于计算器与Microsoft Excel在统计功能部分的编程算法有所不同,故对同一组数据计算结果会有偏差65*运用知识强化练习某一公司为了研究某一类产品的广告费用与其销售额（单位：万元）之间的关系，对多个厂家进行了调查，数据如下：厂家1 2 3 4 5 6 7 8 9 10 广告费ix60 45 35 25 40 20 30 50 25 35 销售额iy520 500 440 380 525 365 475 540 450 385 试求销售额y 关于
36、广告费x 的一元线性回归方程提问巡视指导思考解答及时了解学生知识掌握情况75*理论升华整体建构思考并回答下面的问题：相关关系的定义？相关关系的特点？结论：质疑及 时文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8
37、X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K
38、6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO
39、5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S
40、8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT
41、4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H
42、10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1教学
43、过程教师行为学生行为教学意图时间学生的身高与体重之间存在着一定的关系，这种关系不像象以前研究的函数关系那样，知道身高，就能确定体重的值 但是一般身高的人，体重还是比较大的变量之间的这种非确定性的相互依存的关系叫做相关关系相关关系的特点是，当一个变量或n 个变量的值确定后，另一个变量的值虽然与它（或它们）有着密切的关系，但却无法完全确定归 纳强调回答了 解学 生知 识掌 握情况82*归纳小结强化思想本次课学了哪些内容？重点和难点各是什么？引导回忆*自我反思目标检测本次课采用了怎样的学习方法？你是如何进行学习的？你的学习效果如何？已知某炼钢厂车间每年的利润y 万元与废品率x%的一组统计资料如下废品
44、率 x1.3 1.5 1.6 1.7 1.9 利润 y150 120 110 100 70 求利润 y 关于废品率x 的一元线性回归方程提问巡视指导反思动手求解检验学生学习效果89*继续探索活动探究(1)读书部分：教材(2)书面作业：教材习题10.5 A 组（必做）；10.5 B 组（选做）(3)实践调查：用发现的眼睛寻找生活中具有相关关系变量的实例说明记录分 层次 要求90【教师教学后记】项目反思点学生知识、技能的掌握情况学生是否真正理解有关知识；是否能利用知识、技能解决问题；在知识、技能的掌握上存在哪些问题；学生的情感态度学生是否参与有关活动；在数学活动中，是否认真、积极、自信；文档编码:
45、CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G
46、10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3
47、 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8
48、I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2
49、 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6
50、O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L1文档编码:CZ8X5G10K6B3 HO5F8I4S8R2 ZT4E6O8H10L