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MCS,PHD
Argosy University/ Phoniex University/
Nov-2005 - Oct-2011
Professor
Phoniex University
Oct-2001 - Nov-2016
4.67 Improving SAT scores. Refer to the Chance (Winter 2001) study of students who paid a private tutor (or coach) to help them improve their Scholastic Assessment Test (SAT) scores, Exercise 4.50 (p. 223). Recall that the base-
line model, E(y) = β0 + β1x1 + β2x2, where
y = SAT– Math score, x1 = score on PSAT, and
As an alternative model, the researcher added
several ‘‘control’’ variables, including dummy variables for student ethnicity (x3, x4, and x5), a socioeconomic status index variable (x6), two variables that measured high school performance (x7 and x8), the number of math courses taken in high school (x9), and the overall GPA for the math courses (x10).
(a) Write the hypothesized equation for E(y) for the alternative model.
(b) Give the null hypothesis for a nested model F -test comparing the initial and alternative models.
(c) The nested model F -test, part b, was sta- tistically significant at α = .05. Practically interpret this result.
(d)
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The alternative model, part a, resulted in Ra = .79, βˆ2 = 14, and sβˆ2 = 3. Interpret the value of R2.
(e) Refer to part d. Find and interpret a 95% confidence interval for β2.
(f) The researcher concluded that ‘‘the esti-
mated effect of SAT coaching decreases from the baseline model when control vari- ables are added to the model.’’ Do you agree? Justify your answer.
(g) As a modification to the model of part a, the researcher added all possible interactions between the coaching variable (x2) and the other independent variables in the model. Write the equation for E(y) for this modified model.
(h) Give the null hypothesis for comparing the models, parts a and g. How would you perform this test?
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