1 . 某工厂每日生产一种产品
吨,每日生产的产品当日销售完毕,日销售额为
万元,产品价格随着产量变化而有所变化,经过一段时间的产销,得到了
,
的一组统计数据如下表:
![](https://img.xkw.com/dksih/QBM/2018/5/8/1941134259036160/1942452843610112/STEM/ea27413e1c1c4ae3869d4168c46486ef.png?resizew=349)
(1)请判断
与
中,哪个模型更适合刻画
,
之间的关系?可从函数增长趋势方面给出简单的理由;
(2)根据你的判断及下面的数据和公式,求出
关于
的回归方程,并估计当日产量
时,日销售额是多少?
,
,
,
.
线性回归方程
中,
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cd8127057ac66baff6df79b5f9c35e4.png)
![](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/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://img.xkw.com/dksih/QBM/2018/5/8/1941134259036160/1942452843610112/STEM/ea27413e1c1c4ae3869d4168c46486ef.png?resizew=349)
(1)请判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1db6103cb0f1d2bd6b19235d53ee7e98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0df322f59ef4bfc7b7235e4f15e209b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(2)根据你的判断及下面的数据和公式,求出
![](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/39cc033406da2cdd342308972c6701f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25b136d1d999440d98b75db764ec31f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a376b2827cf12aec528f0a910ee2609f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9c94e3383859e5aad42616625ba24ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a531afc6e63700f1ca2b45d229efb9ea.png)
线性回归方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1db6103cb0f1d2bd6b19235d53ee7e98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6416ea07edbb36301bb6b4ed6787cbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d009860b5581349f59e7274710918273.png)
您最近一年使用:0次
名校
解题方法
2 . 某果园种植“糖心苹果”已有十余年,为了提高利润,该果园每年投入一定的资金,对种植、采摘、包装、宣传等环节进行改进.如图是2009年至2018年,该果园每年的投资金额
(单位:万元)与年利润增量
(单位:万元)的散点图:
该果园为了预测2019年投资金额为20万元时的年利润增量,建立了
关于
的两个回归模型;
模型①:由最小二乘公式可求得
与
的线性回归方程:
;
模型②:由图中样本点的分布,可以认为样本点集中在曲线:
的附近,对投资金额
做交换,令
,则
,且有
,
,
,
.
![](https://img.xkw.com/dksih/QBM/2020/3/17/2421471948890112/2422716055887872/STEM/80fc77da266a46e5b5444930c8227ab7.png?resizew=355)
(1)根据所给的统计量,求模型②中
关于
的回归方程;
(2)分别利用这两个回归模型,预测投资金额为20万元时的年利润增量(结果保留两位小数);
(3)根据下列表格中的数据,比较两种模型的相关指数
,并说明谁的预测值精度更高、更可靠.
附:样本
的最小乘估计公式为
,
;
相关指数
.
参考数据:
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
该果园为了预测2019年投资金额为20万元时的年利润增量,建立了
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
模型①:由最小二乘公式可求得
![](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/6a1d7987a5a81dcf97e0c6f9b73c0605.png)
模型②:由图中样本点的分布,可以认为样本点集中在曲线:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb0027a0822fb984dc68429182c49b72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7ae9d60c249c43595f349d5a092f63f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6970f0219fc7100665928d5f6276de04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb3479bf61fd4d649f2e584d3a5eaf5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6c17ab8a0c633a06a3b2ed8fc6e9305.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0934a8b7d6938ca0630ebeac4da3e845.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea3cd147c347806020c8736a168af621.png)
![](https://img.xkw.com/dksih/QBM/2020/3/17/2421471948890112/2422716055887872/STEM/80fc77da266a46e5b5444930c8227ab7.png?resizew=355)
(1)根据所给的统计量,求模型②中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)分别利用这两个回归模型,预测投资金额为20万元时的年利润增量(结果保留两位小数);
(3)根据下列表格中的数据,比较两种模型的相关指数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c85067c53e936ef32da818efe04bdbb.png)
回归模型 | 模型① | 模型② |
回归方程 | ||
102.28 | 36.19 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/226d2b52caa031a2fa9db35ad1f552a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b33d9063c19ee881cb6be51fe6b83766.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fa16fa102e7d1186183a93447575199.png)
相关指数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5e94f8a8319781aa88a757943151be6.png)
参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0591d9f78b4f4f78c5bd6baaa602ae0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3616e69114889d5d02099b6598a57136.png)
您最近一年使用:0次
2020-03-19更新
|
824次组卷
|
3卷引用:安徽师范大学附属中学2021-2022学年高三上学期12月月考理科数学试题