名校
1 . 为了研究一种昆虫的产卵数
和温度
是否有关,现收集了7组观测数据列于下表中,并做出了散点图,
![](https://img.xkw.com/dksih/QBM/2018/6/6/1961313057177600/1961555457253376/STEM/103cb21b7e974c0e960b0a86d1b66140.png?resizew=274)
发现样本点并没有分布在某个带状区域内,两个变量并不呈现线性相关关系,现分别用模型①
与模型②
作为产卵数
和温度
的回归方程来建立两个变量之间的关系.
其中
,
,
,
,
附:对于一组数据
,
,…,
,其回归直线
的斜率和截距的最小二乘估计分别为:
,
.
(1)根据表中数据,分别建立两个模型下
关于
的回归方程,并在两个模型下分别估计温度为
时的产卵数.(
与估计值均精确到小数点后两位)(参考数据:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d06b5185f92bfcb286d3c9b33581404e.png)
)
(2)若模型①、②的相关指数计算分别为
,请根据相关指数判断哪个模型的拟合效果更好.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://img.xkw.com/dksih/QBM/2018/6/6/1961313057177600/1961555457253376/STEM/103cb21b7e974c0e960b0a86d1b66140.png?resizew=274)
发现样本点并没有分布在某个带状区域内,两个变量并不呈现线性相关关系,现分别用模型①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd64ba05feb903301f70f5e8c56aef60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcdd876f531d502332d984156e1c2f65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
温度 | 20 | 22 | 24 | 26 | 28 | 30 | 32 |
产卵数 | 6 | 10 | 21 | 24 | 64 | 113 | 322 |
400 | 484 | 576 | 676 | 784 | 900 | 1024 | |
1.79 | 2.30 | 3.04 | 3.18 | 4.16 | 4.73 | 5.77 |
26 | 692 | 80 | 3.57 |
1157.54 | 0.43 | 0.32 | 0.00012 |
其中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34f98b6a7f204c9f2584bfe2b872c58e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06d6843acae71eaa561c5a59e0121a9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fb503053c6463545a1b9044043421fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a28d29a4ac419412430571386b03b818.png)
附:对于一组数据
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97112413cae1006fea2e657826d620fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a558626f91e6566a63fcfbbdf87b3d94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef969b96f14388a3a63508a1a2da5f33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9054c1a6cf7743ac2cca8e3caacf0829.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64069762d004a7dfb2e19267b9ca6109.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/044895fcd55c71986e71f8d1bdb25a30.png)
(1)根据表中数据,分别建立两个模型下
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f90d423cb57d9ae42b145bef3124411d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a9a509e9d87fa5449fe61015e57c9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d06b5185f92bfcb286d3c9b33581404e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92320bcdea1e1f1ae42a3ace2072f7ae.png)
(2)若模型①、②的相关指数计算分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9321ab0ceab996a0b606fc142de39d3.png)
您最近一年使用:0次
2018-06-06更新
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334次组卷
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4卷引用:江西省铅山县第一中学2021-2022学年高二下学期开学考试数学(理)试题
江西省铅山县第一中学2021-2022学年高二下学期开学考试数学(理)试题广东省中山市2016-2017学年高二下学期期末统一考试数学(文)试题广东省中山市2016-2017学年高二下学期期末统一考试数学(理)试题(已下线)2018年5月27日 每周一测——《每日一题》2017-2018学年高二理科数学人教选修2-3