Improving SAT scores. Refer to the Chance (Winter 2001) study of students who paid a private tutor (or coach) to help them improve their Standardized Assessment Test (SAT) scores, Exercise 4.50 (p. 223). Recall that multiple regres- sion was used to estimate the effect of coaching on SAT- Mathematics scores, where
y = SAT- Math score
x1 = score on PSAT
x2 = {1 if student was coached, 0 if not}
(a) Write a complete second-order model for E(y) as a function of x1 and x2.
(b) Give the equation of the curve relating E(y) to x1 for noncoached students. Identify the y-intercept, shift parameter, and rate of cur- vature in the equation.
(c) Repeat part b for students who have been coached on the SAT.
(d) How would you test to determine if coaching has an effect on SAT- Math scores?