In the European Union, it has become important to be able to determine an individual's age when legal documentation of the birth date of an individual is unavailable. In the article "Age Estimation in Children by Measurement of Open Apices in Teeth: a European Formula" (International Journal of Legal Medicine [2007]:121: 449-453), researchers developed a model to predict the age, y, of an individual based on the gender of the individual, x1 10 = female, 1 = male2, the height of the second premolar, x2, the number of teeth with root development, x3, and the sum of the normalized heights of seven teeth on the left side of the mouth, x4. The normalized height of the seven teeth was found by dividing the distance between teeth by the height of the tooth. Their model is
y̅ = 9.063 + 0.386x1 + 1.268x2 + 0.676x3 - 0.913x4 - 0.175x3x4
(a) Based on this model, what is the expected age of a female with x2 = 28 mm, x3 = 8, and x4 = 18 mm?
(b) Based on this model, what is the expected age of a male with x2 = 28 mm, x3 = 8, and x4 = 18 mm?
(c) What is the interaction term? What variables interact?
(d) The coefficient of determination for this model is 86.3%. Explain what this means.