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Improving Math SAT scores. Refer to the Chance(Winter
Chapter 12, Problem 158SE(choose chapter or problem)
Problem 158SE
Improving Math SAT scores. Refer to the Chance(Winter 2001) study of students who paid a privatetutor (or coach) to help them improve their ScholasticAssessment Test (SAT) scores, Exercise 2.88 (p. 86).Multiple regression was used to estimate theeffect of coaching on SAT–Mathematics scores. Dataon 3,492 students (573 of whom were coached) wereused to fit the model, E(y) = β0 + β1x1 + β2x2, wherey = SAT9Math score, x1 = score on PSAT, andx2 = {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 astandard error of 3. Use this information to forma 95% confidence interval for β2. Interpret theinterval.
c. Based on the interval, part b, what can you say aboutthe effect of coaching on SAT–Math scores?
d. As an alternative model, the researcher added several “control” variables, including dummy variablesfor student ethnicity (x3, x4, and x5), a socioeconomicstatus index variable (x6), two variables that measured high school performance (x7 and x8), the number of math courses taken in high school (x9), andthe overall GPA for the math courses (x10). Write thehypothesized equation for E(y) for the alternativemodel.
e. Give the null hypothesis for a nested modelF-test comparing the initial and alternativemodels.
f. The nested model F-test, part e, was statistically significant at α = .05. Practically interpret this result.
g. The alternative model, part d, resulted in = .79, = 14, and = 3. Interpret the value of .
h. Refer to part g. Find and interpret a 95% confidenceinterval for β2.
i. The researcher concluded that “the estimated effectof SAT coaching decreases from the baseline modelwhen control variables are added to the model.” Doyou agree? Justify your answer.
j. As a modification to the model of part d, the researcher added all possible interactions between thecoaching variable (x2) and the other independentvariables in the model. Write the equation for E(y) forthis modified model.
k. Give the null hypothesis for comparing the models, parts d and j. How would you perform thistest?
Questions & Answers
QUESTION:
Problem 158SE
Improving Math SAT scores. Refer to the Chance(Winter 2001) study of students who paid a privatetutor (or coach) to help them improve their ScholasticAssessment Test (SAT) scores, Exercise 2.88 (p. 86).Multiple regression was used to estimate theeffect of coaching on SAT–Mathematics scores. Dataon 3,492 students (573 of whom were coached) wereused to fit the model, E(y) = β0 + β1x1 + β2x2, wherey = SAT9Math score, x1 = score on PSAT, andx2 = {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 astandard error of 3. Use this information to forma 95% confidence interval for β2. Interpret theinterval.
c. Based on the interval, part b, what can you say aboutthe effect of coaching on SAT–Math scores?
d. As an alternative model, the researcher added several “control” variables, including dummy variablesfor student ethnicity (x3, x4, and x5), a socioeconomicstatus index variable (x6), two variables that measured high school performance (x7 and x8), the number of math courses taken in high school (x9), andthe overall GPA for the math courses (x10). Write thehypothesized equation for E(y) for the alternativemodel.
e. Give the null hypothesis for a nested modelF-test comparing the initial and alternativemodels.
f. The nested model F-test, part e, was statistically significant at α = .05. Practically interpret this result.
g. The alternative model, part d, resulted in = .79, = 14, and = 3. Interpret the value of .
h. Refer to part g. Find and interpret a 95% confidenceinterval for β2.
i. The researcher concluded that “the estimated effectof SAT coaching decreases from the baseline modelwhen control variables are added to the model.” Doyou agree? Justify your answer.
j. As a modification to the model of part d, the researcher added all possible interactions between thecoaching variable (x2) and the other independentvariables in the model. Write the equation for E(y) forthis modified model.
k. Give the null hypothesis for comparing the models, parts d and j. How would you perform thistest?
ANSWER:
Step 1 of 13
(a)
Interpretation:
The value of 