1 . 某校为了解学生一次考试后数学、物理两个科目的成绩情况,从中随机抽取了25位考生的成绩进行统计分析.25位考生的数学成绩已经统计在茎叶图中,物理成绩如下:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/10/2bdbf01a-125f-460c-b0a9-0026e02a09f8.png?resizew=376)
(Ⅰ)请根据数据在答题卡的茎叶图中完成物理成绩统计;
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/10/e486100f-e9ab-4ad7-9ba2-99806c81e12c.png?resizew=313)
(Ⅱ)请根据数据在答题卡上完成数学成绩的频数分布表及数学成绩的频率分布直方图;
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/10/881b6690-98a7-4ddc-b1a6-0901f93dbe19.png?resizew=251)
(Ⅲ)设上述样本中第i位考生的数学、物理成绩分别为xi,yi(i=1,2,3,…,25).通过对样本数据进行初步处理发现:数学、物理成绩具有线性相关关系,得到:
=86,
=64,
(xi-
)(yi-
)=4698,
(xi-
)2=5524,
≈0.85.求y关于x的线性回归方程,并据此预测当某考生的数学成绩为100分时,该考生的物理成绩(精确到1分).
附:回归直线方程的斜率和截距的最小二乘估计公式分别为:
=
,
=
-
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/10/2bdbf01a-125f-460c-b0a9-0026e02a09f8.png?resizew=376)
(Ⅰ)请根据数据在答题卡的茎叶图中完成物理成绩统计;
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/10/e486100f-e9ab-4ad7-9ba2-99806c81e12c.png?resizew=313)
(Ⅱ)请根据数据在答题卡上完成数学成绩的频数分布表及数学成绩的频率分布直方图;
数学成绩分组 | [50,60﹚ | [60,70﹚ | [70,80﹚ | [80,90﹚ | [90,100﹚ | [100,110﹚ | [110,120] |
频数 |
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/10/881b6690-98a7-4ddc-b1a6-0901f93dbe19.png?resizew=251)
(Ⅲ)设上述样本中第i位考生的数学、物理成绩分别为xi,yi(i=1,2,3,…,25).通过对样本数据进行初步处理发现:数学、物理成绩具有线性相关关系,得到:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fcb21cc59fa1a45e1a0757d59dec092.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/975af18d6d2d55ea017c80865672537a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c4d59dc5995c40c2bfec7e6ef97b72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fcb21cc59fa1a45e1a0757d59dec092.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/975af18d6d2d55ea017c80865672537a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c4d59dc5995c40c2bfec7e6ef97b72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fcb21cc59fa1a45e1a0757d59dec092.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1b5ff691fa14a1db68c8dea50f02e8f.png)
附:回归直线方程的斜率和截距的最小二乘估计公式分别为:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65f4cc6fc3fc8be8989f4cba68e7dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0113bf10c8896146a077243cf1f73dae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d395250b2da9d31f849003a6d05d8b13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/975af18d6d2d55ea017c80865672537a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/439e2a7642a5cc813d0dba4d18a8d2d5.png)
您最近一年使用:0次