Refer to the Chance (Winter 2001) study of students who paid a private tutor (or coach) to help them improve their SAT scores, presented in Exercise. Multiple regression was used to estimate the effect of coaching on SAT-Mathematics scores. Data on 3,492 students (573 of whom were coached) were used to fit the model E(y) = β0 + β1x1 + β2x2, where y = SAT-Math score, x1 = score on PSAT, and x2 = {1 if student was coached, 0 if not}.
a. The fitted model had an adjusted R2 value of .76. Interpret this result.
b. The estimate of β2 in the model was 19, with a standard error of 3. Use this information to form a 95% confidence interval for β2. Interpret the interval.
c. On the basis of the interval you found in part b, what can you say about the effect of coaching on SAT-Math scores?