4.
随着我国经济的发展,居民的储蓄存款逐年增长\(.\)设某地区城乡居民人民币储蓄存款\((\)年底余额\()\)如下表:
年份 | \(2010\) | \(2011\) | \(2012\) | \(2013\) | \(2014\) |
时间代号\(t\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) |
储蓄存款\(y(\)千亿元\()\) | \(5\) | \(6\) | \(7\) | \(8\) | \(10\) |
\((\)Ⅰ\()\)求\(y\)关于\(t\)的回归方程\(\hat{y}=\hat{b}t+\hat{a}\)
\((\)Ⅱ\()\)用所求回归方程预测该地区\(2015\)年\((t=6)\)的人民币储蓄存款.
附:回归方程\(\hat{y}=\hat{b}t+\hat{a}\)中\(\overset{∧}{b}= \dfrac{ \sum\nolimits_{i=1}^{n}\left({t}_{i}- \overset{-}{t}\right)\left({y}_{i}- \overset{-}{y}\right)}{ \sum\limits_{i=1}^{n}{\left({t}_{i}- \overset{-}{t}\right)}^{2}} =\overset{∧}{b}= \dfrac{ \sum\nolimits_{i=1}^{n}{t}_{i}{y}_{i}-n \overset{-}{t} \overset{-}{y}}{ \sum\limits_{i=1}^{n}t_{i}^{2}-n{ \overset{-}{t}}^{2}} \overset{∧}{a}= \overset{-}{y}- \overset{∧}{b} \overset{-}{t} \)