The estimate of beta2nbspin the model was 19 with a

Question

Improving SAT scores

Chance (Winter 2001) published a study of students who paid a private tutor (or coach) to help them improve their Scholastic Assessment Test (SAT) scores. 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) Based on the interval, part b, what can you say about the effect of coaching on SAT-Math scores?