The Staff of a Test Kitchen Is Attempting to Determine $\text { Baking Times of Roasts }$

question 55

Essay

The staff of a test kitchen is attempting to determine the baking time, y, of a roast, i.e., the time it takes the internal temperature of the roast to reach 165°F, using two variables, the temperature setting of the oven, x1, and the weight of the roast, x2, in pounds. The data for 24 roasts are shown below. $\text { Baking Times of Roasts }$
$\begin{array}{lll|lll|lll|llll}\mathrm{X} 1\left({ }^{\circ} \mathrm{F}\right) & \mathrm{X} 2(\mathrm{lb}) & \mathrm{Y}(\mathrm{hr}) & \mathrm{X} 1\left({ }^{\circ} \mathrm{F}\right) & \mathrm{X} 2(\mathrm{lb}) & \mathrm{Y}(\mathrm{hr}) & \mathrm{X} 1\left({ }^{\circ} \mathrm{F}\right) & \mathrm{X} 2(\mathrm{lb}) & \mathrm{Y}(\mathrm{hr}) & \mathrm{X} 1\left({ }^{\circ} \mathrm{F}\right) & \mathrm{X} 2(\mathrm{lb}) &\mathrm{Y}(\mathrm{hr}) \\\hline 300 & 2.2 & 2.6 & 325 & 2.1 & 2.3 & 350 & 2.3 & 2.2 & 375 & 2.2 & 1.9 \\300 & 2.7 & 2.8 & 325 & 2.4 & 2.4 & 350 & 2.5 & 2.3 & 375 & 2.6 & 2.2 \\300 & 2.9 & 3.1 & 325 & 2.9 & 2.6 & 350 & 2.8 & 2.5 & 375 & 2.9 & 2.4 \\300 & 3.1 & 3.2 & 325 & 3.0 & 2.7 & 350 & 3.2 & 2.7 & 375 & 3.1 & 2.6 \\300 & 3.2 & 3.2 & 325 & 3.2 & 2.9 & 350 & 3.4 & 2.8 & 375 & 3.3 & 2.7 \\300 & 3.5 & 3.3 & 325 & 3.6 & 3.1 & 350 & 3.5 & 2.8 & 375 & 3.4 & 2.7\end{array}$
a. Fit a complete second-order model to the data. b. Do the data provide sufficient evidence to indicate that the second-order terms contribute information for the prediction of y? State the null and alternative hypotheses and the test statistic. Use α = .05. 12.10 Stepwise Regression (Optional) 1 Understand and Interpret Stepwise Regression Model