The Table Shows the Profit Y (In Thousands of Dollars)

Essay

The table shows the profit y (in thousands of dollars) that a company made during a month when the price of its product was x dollars per unit.

$\begin{array}{cc}\hline \text { Profit, } y & \text { Price, } x \\\hline 12 & 1.20 \\17 & 1.25 \\20 & 1.29 \\21 & 1.30 \\24 & 1.35 \\26 & 1.39 \\27 & 1.40 \\23 & 1.45 \\21 & 1.49 \\20 & 1.50 \\15 & 1.55 \\11 & 1.59 \\10 & 1.60 \\5 & 1.65 \\\hline\end{array}$

a. Fit the model $y = \beta _ { 0 } + \beta _ { 1 } x + \beta _ { 2 } x 2 + \varepsilon$ to the data and give the least squares prediction equation.
b. Plot the fitted equation on a scattergram of the data.
c. Is there sufficient evidence of downward curvature in the relationship between profit and price? Use $\alpha = .05$ .