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解题方法
1 . 为调查某地区植被覆盖面积x(单位:公顷)和野生动物数量y的关系,某研究小组将该地区等面积划分为200个区块,从中随机抽取20个区块,得到样本数据
,部分数据如下:
经计算得:
,
,
,
.
(1)利用最小二乘法估计建立y关于x的线性回归方程
;
(2)该小组又利用这组数据建立了x关于y的线性回归方程
,并把这两条拟合直线画在同一坐标系xOy下,横坐标x,纵坐标y的意义与植被覆盖面积x和野生动物数量y一致.
(i)求这两条直线的公共点坐标.
(ii)比较
与
的斜率大小,并证明.
附:y关于x的线性回归方程
中.
,
,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7fe74f980aed854fd0c87ccd22c01f8.png)
x | … | 2.7 | 3.6 | 3.2 | … |
y | … | 57.8 | 64.7 | 62.6 | … |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bbef9a78530633bceaa0e326f4641c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d7d61b0eb6ab51face6b77f35b8569d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a94e1831a774131711f5003f265ffad5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/600e1841f12a24ddbcc553c84e73bb2a.png)
(1)利用最小二乘法估计建立y关于x的线性回归方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
(2)该小组又利用这组数据建立了x关于y的线性回归方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
(i)求这两条直线的公共点坐标.
(ii)比较
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
附:y关于x的线性回归方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9cf74bbdee085c44778ac6191e5016b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2dbdbf02e0dd324daba7488c3e3bf31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a58291bd91befe1061530246da983727.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3ae9421919944d997c304d7711b4b67.png)
您最近一年使用:0次
2 . 已知函数
.
(1)证明:
;
(2)当
时,
,求
的取值范围.
![](https://img.xkw.com/dksih/QBM/2016/3/21/1572548303912960/1572548309950464/STEM/00c5466bcd85458fbfed86d711069741.png)
(1)证明:
![](https://img.xkw.com/dksih/QBM/2016/3/21/1572548303912960/1572548309950464/STEM/cb6f7fccfbf74ae0a57a20b073c00e57.png)
(2)当
![](https://img.xkw.com/dksih/QBM/2016/3/21/1572548303912960/1572548309950464/STEM/8eaf6ceb221e4653979aaf54982d43a8.png)
![](https://img.xkw.com/dksih/QBM/2016/3/21/1572548303912960/1572548309950464/STEM/82c53adcfbad4c2ea3443899ac587edf.png)
![](https://img.xkw.com/dksih/QBM/2016/3/21/1572548303912960/1572548309950464/STEM/d214db008944432a8397a913d2652168.png)
您最近一年使用:0次