某企业为确定在2019年度投入某种产品的开发费用,需了解年开发费用
(单位:百万元)对年销售量
(单位:百万件)的影响,统计了近8年投入的年开发费用
与年销售量
(![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5f2634766a7356255d9426013f69bc5.png)
)的数据,得到如下散点图.根据散点图可得年开发费用
和年销售量
符合
(其中
为大于0的常数)的回归方程.
![](https://img.xkw.com/dksih/QBM/2022/3/24/2943260542443520/2947889931558912/STEM/df0e7e6171384a6c87f77c4b18cdde37.png?resizew=338)
(1)对数据作如下处理:
,两边取对数得
,令
,得到相关统计量的值如下表,求
关于
的回归方程;
(2)已知企业年利润
(单位:百万元)与
的关系为
(其中
)根据(1)的结果,要使得该企业2019年的年利润最大,预计2019年应投入多少开发费用?
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
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.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/f5f2634766a7356255d9426013f69bc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2134fc8169d224141b646cfcb70c4a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fea788ae8bd9c0cc3924d1d051d3363c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://img.xkw.com/dksih/QBM/2022/3/24/2943260542443520/2947889931558912/STEM/df0e7e6171384a6c87f77c4b18cdde37.png?resizew=338)
(1)对数据作如下处理:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e669003697300730a70f6fa2d2a035ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b41ac9a19a9260cd504784976200cc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6363919698a207f13390fa7405c85cc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
24.40 | 12 | 12 | 37.20 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/145a1614b27db531b410a3bb1f427552.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11204e2fb6e560bf7a4ca26eaebfc526.png)
附:对于一组数据
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cbf40ba2349bb461db69fca44994572.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5954e038f4244e7bf6b1e0d6d5554884.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e5531913e2f170465d8df01795cd51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7235fc68789bd371e118433de5b0460.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0943f70585435955d528325e51ef013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6adf5e1e882ad52e11a95a0f671f20f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf2c6df1d1a621ca7cb7c4eaf7de5f65.png)
更新时间:2022-03-31 08:00:19
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【推荐2】已知函数
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(1)求
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(2)求
的单调区间;
(3)若
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(1)求
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(2)求
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(3)若
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名校
解题方法
【推荐3】已知函数
.
(1)当
时,求f(x)的最小值;![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e45bcd8f6ede8cc2513ad41402f40086.png)
(2)设
为整数,且对于任意正整数
,
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c83e99119d426e266f76b858b0bfb1e5.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e45bcd8f6ede8cc2513ad41402f40086.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8339e6f70847fc5c196d0b2fc3fc6d89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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解答题-问答题
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(0.65)
名校
【推荐1】某企业积极响应“碳达峰”号召,研发出一款性能优越的新能源汽车,备受消费者青睐.该企业为了研究新能源汽车在某地区每月销售量
(单位:千辆)与月份
的关系,统计了今年前5个月该地区的销售量,得到下面的散点图及一些统计量的值.
表中
.
(1)根据散点图判断两变量
的关系用
与
哪一个比较合适?(给出判断即可,不必说明理由)
(2)根据(1)的判断结果及表中数据,建立
关于
的回归方程(
的值精确到
),并预测从今年几月份起该地区的月销售量不低于
万辆?
附:对于一组数据
,其回归直线方程
的斜率和截距的最小二乘法估计分别为
.
![](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/d97a1454ac85ee201055d8e55cedef48.png)
(1)根据散点图判断两变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6a5b1c19e4c57f1d259f8269e551c64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb5b75998316104f379d131d55957ff1.png)
(2)根据(1)的判断结果及表中数据,建立
![](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/5cd40bb3c1159beb697abfb5e5f5544a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a87796ee30e6c5d5e6b6285b32abe10c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/900206075ce8f1f040d2e3a6685ad51a.png)
附:对于一组数据
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eafbe64ec9acf78f3624abbd06d516e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1db6103cb0f1d2bd6b19235d53ee7e98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/446c21b8025405469a473aa0b32f9373.png)
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【推荐2】某企业生产一种产品,从流水线上随机抽取
件产品,统计其质量指标值并绘制频率分布直方图(如图1):规定产品的质量指标值在
的为劣质品,在
的为优等品,在
的为特优品,销售时劣质品每件亏损
元,优等品每件盈利
元,特优品每件盈利
元,以这
件产品的质量指标值位于各区间的频率代替产品的质量指标值位于该区间的概率.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/22/816272a4-81c1-41d3-8dcd-e540c7586d8f.png?resizew=363)
(1)求每件产品的平均销售利润;
(2)该企业主管部门为了解企业年营销费用
(单位:万元)对年销售量
(单位:万件)的影响,对该企业近
年的年营销费用
和年销售量
,
数据做了初步处理,得到的散点图(如图2)及一些统计量的值.
表中
,
,
,
.
根据散点图判断,
可以作为年销售量
(万件)关于年营销费用
(万元)的回归方程.
①求
关于
的回归方程;
②用所求的回归方程估计该企业每年应投入多少营销费,才能使得该企业的年收益的预报值达到最大?(收益
销售利润
营销费用,取
)
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
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0efba7147f5b9ced8bc4a72f0a9fb8af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3cebcf88e22ba150498cb3fb00a79e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa309485eb0b1817c52ab75a52f6a3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/973e00aa2cd62d4694bc5fcaa16cd807.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66577f4cb97c0d2a213ab1a9a02d1324.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0efba7147f5b9ced8bc4a72f0a9fb8af.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/22/816272a4-81c1-41d3-8dcd-e540c7586d8f.png?resizew=363)
(1)求每件产品的平均销售利润;
(2)该企业主管部门为了解企业年营销费用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.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/a0405de2f5dff1a2ee2fe7ac261c52a6.png)
![]() | ![]() | ![]() | ![]() |
![]() | ![]() | ![]() | ![]() |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90229c4f76db5de308cf8d5fc382099b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53c26fa1e573812fab6a173a4eb0ed38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e0c311fc644b7c09c3dbdfbb3bc35bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632515907518a50055393a1d3060630a.png)
根据散点图判断,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7517fe51db28d471885070007f67becf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
②用所求的回归方程估计该企业每年应投入多少营销费,才能使得该企业的年收益的预报值达到最大?(收益
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6706fe00b4e231e62d9ecbec567d526b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bfc339cf6dd66599db64fa3fa44e608.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/024365db61bdf55ee24e5d5cbecca5f7.png)
附:对于一组数据
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf1c6aadc0129bf86f4fff9dcfb924b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/154100371e025fffe0ffae8be9567383.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a14e40329de36fc4a1a3f8fbfafda12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0940cc781cd9cb5c05a3795acec775cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abf334c4639c849a3566c235fd433d9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/815e2869dc16e2ae7a7e1911e3afc8c3.png)
您最近一年使用:0次
解答题-证明题
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适中
(0.65)
解题方法
【推荐3】我市物价监督部门为调研某公司新开发上市的一种产品销售价格的合理性,对该公司的产品的销售与价格进行了统计分析,得到如下数据和散点图:
![](https://img.xkw.com/dksih/QBM/2018/7/8/1984043695022080/1985696665444352/STEM/dfd2d1450f7840728d35a38fbd33bec9.png?resizew=283)
![](https://img.xkw.com/dksih/QBM/2018/7/8/1984043695022080/1985696665444352/STEM/74c62cb4e2564ff6ad80248cb1a15e03.png?resizew=246)
图①为
散点图,图②为
散点图.
(1)根据散点图判断
与
,
与
哪一对具有较强的线性相关性(不必证明);
(2)根据(1)的判断结果和参考数据,建立
关于
的回归方程(线性回归方程中的斜率和截距均保留两位有效数字);
(3)定价为多少时,年销售额的预报值最大?(注:年销售额
定价
年销售)
参考数据:
,
,
,
,
,
,
,
,
参考公式:
,
.
定价 | 10 | 20 | 30 | 40 | 50 | 60 |
年销售 | 1150 | 643 | 424 | 262 | 165 | 86 |
14.1 | 12.9 | 12.1 | 11.1 | 10.2 | 8.9 |
![](https://img.xkw.com/dksih/QBM/2018/7/8/1984043695022080/1985696665444352/STEM/dfd2d1450f7840728d35a38fbd33bec9.png?resizew=283)
![](https://img.xkw.com/dksih/QBM/2018/7/8/1984043695022080/1985696665444352/STEM/74c62cb4e2564ff6ad80248cb1a15e03.png?resizew=246)
图①为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/059d6df06a5b85848dc4fa33327f8e07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b2ac3c788485a6df6fdfcd513f4bee4.png)
(1)根据散点图判断
![](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/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)根据(1)的判断结果和参考数据,建立
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(3)定价为多少时,年销售额的预报值最大?(注:年销售额
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6706fe00b4e231e62d9ecbec567d526b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2468403b3eba9e40bfa36f464e927738.png)
参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e54eed940d0b8e9d9e7aeb0928555d3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbf4fe547c4331eec61d6656c6066001.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06b5378455bfe4e7edce54bc29a67cbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0350fbacb82bf53dcdaea2d7d928fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0c7c56a0df2170299dadbb19acb5b2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f92517f6cef3bd70d490283df2435030.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef8655b5cbc7dd0d9da80e0c491a7254.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82526ed65e2e79a9a8e842e1d03e9f2e.png)
参考公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d60ab8ba460ad6d95b1363e27f335694.png)
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