Question Details

(Solution) - Multiple regression was used to estimate the effect of coaching

Brief item decscription

Solution download

Item details:

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) = ?0 + ?1x1 + ?2x2, 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 ?2 in the model was 19, with a standard error of 3. Use this information to form a 95% confidence interval for ?2. Interpret the interval.
c. Based on the interval, part b, what can you say about the effect of coaching on SAT-Math scores?
d. 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 (xl0). Write the hypothesized equation for E(y) for the alternative model.
e. Give the null hypothesis for a nested model F-test comparing the initial and alternative models.
f. The nested model F-test. part e, was statistically significant at ? = .05. Practically interpret this result.
g. The alternative model, part d, resulted in R2a = .79, 2 = 14, and s2= 3. Interpret the value of R2a.
h. Refer to part g. Find and interpret a 95% confidence interval for ?2.
i. The researcher concluded that "the estimated effect of SAT coaching decreases from the baseline model when control variables are added to the model." Do you agree? Justify your answer.
j. As a modification to the model of part d, 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.
k. Give the null hypothesis for comparing the models, parts d and j. How would you perform this test?
For information: 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 2.88.


About this question:

This question was answered on: Jul 11, 2017

PRICE: $15 (18.37 KB)

Buy this answer for only: $15

Pay using PayPal (No PayPal account Required) or your credit card. All your purchases are securely protected by PayPal.

Need a similar solution fast, written anew from scratch? Place your own custom order

We have top-notch tutors who can help you with your essay at a reasonable cost and then you can simply use that essay as a template to build your own arguments. This we believe is a better way of understanding a problem and makes use of the efficiency of time of the student. New solution orders are original solutions and precise to your writing instruction requirements. Place a New Order using the button below.

Order Now