真题
1 . 从某居民区随机抽取10个家庭,获得第i个家庭的月收入xi(单位:千元)与月储蓄yi(单位:千元)的数据资料,算得
,
,
,
.
(1)求家庭的月储蓄y对月收入x的线性回归方程y=bx+a;
(2)判断变量x与y之间是正相关还是负相关;
(3)若该居民区某家庭月收入为7千元,预测该家庭的月储蓄.
附:线性回归方程y=bx+a中,
,
,其中
,
为样本平均值,线性回归方程也可写为
.
![](https://img.xkw.com/dksih/QBM/2014/5/30/1571743652904960/1571743658598400/STEM/f6aad3c722b247f8a377496372c521af.png)
![](https://img.xkw.com/dksih/QBM/2014/5/30/1571743652904960/1571743658598400/STEM/c320a21a443749439fcf51d1c3e121e8.png)
![](https://img.xkw.com/dksih/QBM/2014/5/30/1571743652904960/1571743658598400/STEM/dba0e4355d95474a980f2639b8b4e06d.png)
![](https://img.xkw.com/dksih/QBM/2014/5/30/1571743652904960/1571743658598400/STEM/1b7d9d8de25845b89036b3d8ffefc27f.png)
(1)求家庭的月储蓄y对月收入x的线性回归方程y=bx+a;
(2)判断变量x与y之间是正相关还是负相关;
(3)若该居民区某家庭月收入为7千元,预测该家庭的月储蓄.
附:线性回归方程y=bx+a中,
![](https://img.xkw.com/dksih/QBM/2014/5/30/1571743652904960/1571743658598400/STEM/28f077dcb91649958914e58602c2ef21.png)
![](https://img.xkw.com/dksih/QBM/2014/5/30/1571743652904960/1571743658598400/STEM/391aca1bdea449eb9827c025f35bff93.png)
![](https://img.xkw.com/dksih/QBM/2014/5/30/1571743652904960/1571743658598400/STEM/059771293f034304a2b6d3691ab8639c.png)
![](https://img.xkw.com/dksih/QBM/2014/5/30/1571743652904960/1571743658598400/STEM/17c118b34b1c426cb86d52f7ff957e28.png)
![](https://img.xkw.com/dksih/QBM/2014/5/30/1571743652904960/1571743658598400/STEM/2faaae0bfedc45d5a1059c9670f0747f.png)
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