5.某种产品的广告费用支出X与销售额之间有如下的对应数据:
(1)画出散点图;
(2)求回归直线方程;
(3)据此估计广告费用为10销售收入y的值.
参考公式:最小二乘法得$\left\{\begin{array}{l}{\widehat{b}=\frac{\sum_{i=1}^{n}({x}_{i}-\overline{x})({y}_{i}-\overline{y})}{\sum_{i=1}^{n}({x}_{i}-\overline{x})^{2}}=\frac{\sum_{i=1}^{n}{x}_{i}{y}_{i}-n\overline{x}\overline{y}}{\sum_{i=1}^{n}{{x}_{i}}^{2}-n\overline{{x}^{2}}}}\\{\widehat{a}=\overline{y}-\widehat{b}\overline{x}}\end{array}\right.$其中:$\widehat{b}$是回归方程的斜率,$\widehat{a}$是截距.
0 251635 251643 251649 251653 251659 251661 251665 251671 251673 251679 251685 251689 251691 251695 251701 251703 251709 251713 251715 251719 251721 251725 251727 251729 251730 251731 251733 251734 251735 251737 251739 251743 251745 251749 251751 251755 251761 251763 251769 251773 251775 251779 251785 251791 251793 251799 251803 251805 251811 251815 251821 251829 266669
| x | 2 | 4 | 5 | 6 | 8 |
| y | 30 | 40 | 60 | 50 | 70 |
(2)求回归直线方程;
(3)据此估计广告费用为10销售收入y的值.
参考公式:最小二乘法得$\left\{\begin{array}{l}{\widehat{b}=\frac{\sum_{i=1}^{n}({x}_{i}-\overline{x})({y}_{i}-\overline{y})}{\sum_{i=1}^{n}({x}_{i}-\overline{x})^{2}}=\frac{\sum_{i=1}^{n}{x}_{i}{y}_{i}-n\overline{x}\overline{y}}{\sum_{i=1}^{n}{{x}_{i}}^{2}-n\overline{{x}^{2}}}}\\{\widehat{a}=\overline{y}-\widehat{b}\overline{x}}\end{array}\right.$其中:$\widehat{b}$是回归方程的斜率,$\widehat{a}$是截距.