2.
某种产品的广告费支出\(x\)与销售额\(y\)\((\)单位:万元\()\)之间有如下对应数据:
\(x\) | \(2\) | \(4\) | \(5\) | \(6\) | \(8\) |
\(y\) | \(30\) | \(40\) | \(60\) | \(50\) | \(70\) |
\((\)Ⅰ\()\)求回归直线方程\(\hat{y}=\hat{b}x+\hat{a}\),其中\(\begin{matrix} & \hat{b}=\dfrac{\sum\limits_{i=1}^{n}{({{x}_{i}}-\bar{x})({{y}_{i}}-\bar{y})}}{\sum\limits_{i=1}^{n}{{{({{x}_{i}}-\bar{x})}^{2}}}}=\dfrac{\sum\limits_{i=1}^{n}{{{x}_{i}}{{y}_{i}}-n\bar{x}\cdot \bar{y}}}{\sum\limits_{i=1}^{n}{{{x}_{i}}^{2}-n{{{\bar{x}}}^{2}}}},\hat{a}=\bar{y}-\hat{b}\bar{x} \\ & \\ \end{matrix}\)
\((\)Ⅱ\()\)试预测广告费支出为\(10\)万元时,销售额多大?
\((\)参考公式和数据:\(\sum\limits_{i=1}^{5}{x_{i}^{2}}=145\) \(\sum\limits_{i=1}^{5}{y_{i}^{2}}=13500\) \(\sum\limits_{i=1}^{5}{{{x}_{i}}{{y}_{i}}=1380})\)