Monthly Total Production Costs and the Number of Units Produced

Essay

Monthly total production costs and the number of units produced at a local company over a period of 10 months are shown below. $$\begin{array} { ccc } \text { Month } & \text { Production Costs } \left( y _ { i } \right) & \text { Units Produced } \left( x _ { 1 } \right) \\&(\$ \text { millions) } &(\text { millions) } \\1 & 1 & 2 \\2 & 1 & 3 \\3 & 1 & 4 \\4 & 2 & 5 \\5 & 2 & 6 \\6 & 4 & 7 \\7 & 5 & 8 \\8 & 7 & 9 \\9 & 9 & 10 \\10 & 12 & 10\end{array}$$ Use Excel's Regression tool to estimate a second-order model of the form $$y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 1 } ^ { 2 } + \varepsilon$$ ​