12.62 Academic performance and participation in extracurricular activities Let y = grade point average (GPA) and x =

number of times a student has participated in extracurricular activities, measured for all students at a university.

Explain the mean and variability about the mean aspects of the regression model my = a + bx in the context of these variables. In your answer, explain why

(a) it is more sensible to let a + bx represent the means of the conditional distributions rather than individual observations,

(b) the model allows variation around the mean with its s parameter.