2.
为了调查历城区城乡居民人民生活水平,随机抽取了\(10\)个家庭,得到第\(i(i{=}1{,}2{,}{…}{,}10)\)个家庭月收入\(x_{i}(\)单位:千元\()\)与月流动资金\(y_{i}(\)单位:千元\()\)的数据资料如下表:
\(\sum_{i{=}1}^{10}x_{i}\) | \(\sum_{i{=}1}^{10}y_{i}\) | \(\sum_{i{=}1}^{10}\omega_{i}\) | \(\sum_{i{=}1}^{10}x_{i}y_{i}\) | \(\sum_{i{=}1}^{10}\omega_{i}y_{i}\) |
\(720\) | \(20\) | \(80\) | \(196\) | \(184\) |
其中\(\omega_{i}{=}\sqrt{x_{i}}{,}y\)与\(x\)满足函数模型\(y{=}d{+}c\sqrt{x}\);
\((\)Ⅰ\()\)求方程\(y{=}d{+}c\sqrt{x}\);
\((\)Ⅱ\()\)已知某家庭\(9\)月收入为\(9\)千元,该家庭计划用当月流动资金购置价格为\(499\)元的九阳豆浆机,问计划能否成功?
附:对一组数据\((x_{i}{,}y_{i})(i{=}1{,}2{,}{…}{,}10)\),其回归直线\(y{=}\hat{b}x{+}\hat{a}\)的最小二乘法估计为
\(b= \dfrac{ \sum\nolimits_{i=1}^{n}{x}_{i}{y}_{i}-n \bar{xy}}{ \sum\nolimits_{i=1}^{n}{{x}_{i}}^{2}-n{ \bar{x}}^{2}},a= \bar{y}-b \bar{x} \)