1 . 某地区不同身高
的未成年男性的体重平均值
如下表:
已知
与
之间存在很强的线性相关性,
(Ⅰ)据此建立
与
之间的回归方程;
(Ⅱ)若体重超过相同身高男性体重平均值的
倍为偏胖,低于
倍为偏瘦,那么这个地区一名身高
体重为
的在校男生的体重是否正常?
参考数据:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c7a037bbc5eaa5ae254c534cddcb89d.png)
附:对于一组数据
,其回归直线
中的斜率和截距的最小二乘估计分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e30c5601526349a45342c9360c002be6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e2b0a9038d6c59a67ac9b7b68e23d69.png)
身高x(cm) | 60 | 70 | 80 | 90 | 100 | 110 | 120 | 130 | 140 |
体重y(kg) | 6.13 | 7.90 | 9.99 | 12.15 | 15.02 | 17.50 | 20.92 | 26.86 | 31.11 |
已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/107e729f34ccfe61721cd38e34028b7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(Ⅰ)据此建立
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(Ⅱ)若体重超过相同身高男性体重平均值的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39bdd8cfcced9f149d6912858bc4d4e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b418f716e6ea876faa7b003b8af56044.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34343b02ec67b326a8e746840f1456ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7e9a6034ba2b650794325141cbd1e50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd1c9b733d89a021d7c9f56f85e8b9e2.png)
参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c7a037bbc5eaa5ae254c534cddcb89d.png)
附:对于一组数据
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aec0e1edbc352a37e0221ed4275a70c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa44019c321952811401dd9a9bad9e0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1589dd2838890c5a146887d9d0ac85c.png)
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