名校
解题方法
1 . 为响应党中央“扶贫攻坚”的号召,某单位指导一贫困村通过种植紫甘薯来提高经济收入.紫甘薯对环境温度要求较高,根据以往的经验,随着温度的升高,其死亡株数成增长的趋势.下表给出了2021年种植的一批试验紫甘薯在温度升高时6组死亡的株数.
经计算,
,
,
,
,
,
,
,其中
,
分别为试验数据中的温度和死亡株数,
.
(1)若用一元线性回归模型,求
关于
的经验回归方程
;
(2)若用非线性回归模型求得
关于
的非线性经验回归方程
,且相关指数为
.
(ⅰ)试与(1)中的回归模型相比,用
说明哪种模型的拟合效果更好;
(ii)用拟合效果好的模型预测温度为35℃时该批紫甘薯的死亡株数(结果取整数).
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:
,
;相关指数为:
.
温度![]() | 21 | 23 | 24 | 27 | 29 | 30 |
死亡数![]() | 6 | 11 | 20 | 27 | 57 | 77 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19a422afb736f11477fcabac92fafff2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da3a94fb32ba570eba2d310029b611ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e87f7b5a1d435585aa25465acdf803f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c44743edf1ff8b6bf0d57f8da3b834dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cfff66a075cf1b8b1ad9b9f758afe27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0552e0b7e4ce7469aa42ce6acea48566.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8daf7f8f39c2a7d5016bec69d4db45a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ea8f47d8d8d9e1832d52b1c7425450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4de122ae929b1acaff321dec137622ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5b700bb0dd6bb46e61670aa797279b6.png)
(1)若用一元线性回归模型,求
![](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/1db6103cb0f1d2bd6b19235d53ee7e98.png)
(2)若用非线性回归模型求得
![](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/893f69cb490ba1d909540bb30cb10d30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8890b18de650ddfc0f38de13694d774b.png)
(ⅰ)试与(1)中的回归模型相比,用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c85067c53e936ef32da818efe04bdbb.png)
(ii)用拟合效果好的模型预测温度为35℃时该批紫甘薯的死亡株数(结果取整数).
附:对于一组数据
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49111de9519520c5d8ac4e376244232b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1db6103cb0f1d2bd6b19235d53ee7e98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5ff9da673de8a187cbf3d8821ac542d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a58291bd91befe1061530246da983727.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed89d4a96f55f8b9d132424a9738534c.png)
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2022-05-23更新
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6卷引用:西藏自治区拉萨中学2023届高三下学期3月数学(理)检测试题