The Staff of a Test Kitchen Is Attempting to Determine $y$

question 68

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 $165^{\circ} \mathrm{F}$ , using two variables, the temperature setting of the oven, $x_{1}$ , and the weight of the roast, $x_{2}$ , in pounds. The data for 24 roasts are shown below.

$\text { Baking Times of Roasts }$


a. $\text { Fit a complete second-order model to the data. }$
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 hypothes

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Definitions:

Oral Cavity

The oral cavity refers to the mouth, an opening in the body used for eating, breathing, and vocalizing, encompassing structures such as the teeth, tongue, and palate.

Tobacco Smoke

The smoke produced by burning tobacco products, containing a mix of harmful chemicals and carcinogens.

Respiratory Infections

Diseases caused by pathogens affecting the lungs and airways, which can interfere with breathing.

Carcinogens

Agents capable of causing cancer in living tissue by altering cellular metabolism or damaging genetic material directly.