Researchers developed a model to predict the age, \(y\), of an individual based on the gender of the individual, \(x_{1}(0=\) female, \(1=\) male \()\), the height of the second premolar, \(x_{2}\), the number of teeth with root development, \(x_{3}\), and the sum of the normalized heights of seven teeth on the left side of the mouth, \(x_{4}\). The normalized height of the seven teeth was found by dividing the distance between teeth by the height of the tooth. The model was

\(\hat{y}=9.101+0.381 x_{1}+1.254 x_{2}+0.658 x_{3}-0.919 x_{4}-0.171 x_{3} x_{4}\)

(a) Based on this model, what is the expected age of a female with \(x_{2}=25 \mathrm{~mm}, x_{3}=7\), and \(x_{4}=15 \mathrm{~mm}\) ?

(b) Based on this model, what is the expected age of a male with \(x_{2}=25 \mathrm{~mm}, x_{3}=7\), and \(x_{4}=15 \mathrm{~mm}\) ?

(c) What is the interaction term? What variables interact?

(d) The coefficient of determination for this model is \(83.8 \%\). Explain what this means.
\[\begin{aligned}& H_{0} \text { : the sequence of data is random. } \\& H_{1} \text { : the sequence of data is not random. }\end{aligned}\]