Homework Help is Here – Start Your Trial Now!
Math
Statistics
Consider the following model to explain the percentage of students receiving a passing score on a math test (math4) at Michigan schools math4 = B₁ + B₁ log(expend) + 3₂ log(enroll) + 3zlunch + u (1)

Consider the following model to explain the percentage of students receiving a passing score on a math test (math4) at Michigan schools math4 = B₁ + B₁ log(expend) + 3₂ log(enroll) + 3zlunch + u (1)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
See similar textbooks
icon
Related questions
Question

question c

4. Consider the following model to explain the percentage of students receiving a passing score on a math test (math4) at Michigan schools math4 =B₁ + B₁ log(expend) + ß₂log(enroll) + Bzlunch + u (1) 2 where expend is total school expenditure, enroll is the number of students at the school and lunch is the percentage of students who are eligible for the school free lunch program. Using a sample of 1823 schools we have found the following results: math4 46.19+8.53 log(expend) - 13.37 log(enroll) - 0.471lunch (1.80) (0.014) (17.91) (1.84) n = 1823, R² = 0.380 (a) Interpret the estimated coefficient on log(expend). Why do you think that the estimated coefficient on lunch is negative? (b) Test the overall significance of the regression. (c) Next year, the number of students is expected to increase by 1%. An economist states that if the total school expenditure also increases by 1%, the 1% increase in the number of students will have no effect on the percentage of students who pass the exam. Write down the null and the alternative hypotheses to test the economist's statement. What would be the restricted model after imposing the null hypothesis?
Transcribed Image Text:4. Consider the following model to explain the percentage of students receiving a passing score on a math test (math4) at Michigan schools math4 =B₁ + B₁ log(expend) + ß₂log(enroll) + Bzlunch + u (1) 2 where expend is total school expenditure, enroll is the number of students at the school and lunch is the percentage of students who are eligible for the school free lunch program. Using a sample of 1823 schools we have found the following results: math4 46.19+8.53 log(expend) - 13.37 log(enroll) - 0.471lunch (1.80) (0.014) (17.91) (1.84) n = 1823, R² = 0.380 (a) Interpret the estimated coefficient on log(expend). Why do you think that the estimated coefficient on lunch is negative? (b) Test the overall significance of the regression. (c) Next year, the number of students is expected to increase by 1%. An economist states that if the total school expenditure also increases by 1%, the 1% increase in the number of students will have no effect on the percentage of students who pass the exam. Write down the null and the alternative hypotheses to test the economist's statement. What would be the restricted model after imposing the null hypothesis?
Expert Solution
steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS