Let grad be a dummy variable for whether a student-athlete at a large university graduates in five Let hsGPA and SAT be high school grade point average and SAT score, respectively. Let study be the number of hours spent per week in an organized study hall. years. O Let 0(. ) be the standard normal cumulative distribution function and (.) be the standard normal density function. Please write down the Probit model to describe the probability of graduating in five years in terms of hsGPA, SAT and study. Please write down the partial effect of study on P(grad = 1|hsGPA, SAT, study). %3D (ii) If we use a Linear Probability Model instead, write down the model that you'll estimate. What limitations does this model have? (iii) Suppose that, using data on 420 student-athletes, the following logit model is obtained: P(grad = 1|hsGPA, SAT, study) = A(-1.17+ .24hsGPA+ .00058SAT + .073study) where A(z) = exp(z)[1+ exp(z)]. Please give the expressions for P(grad = 1|hsGPA,SAT,study) P(grad = 0|hsGPA,SAT,study) P(grad = 1|hsGPA,SAT,study) log 1-P(grad = 1|hsGPA,SAT,study) and Please show your work as detailed as possible.
Let grad be a dummy variable for whether a student-athlete at a large university graduates in five Let hsGPA and SAT be high school grade point average and SAT score, respectively. Let study be the number of hours spent per week in an organized study hall. years. O Let 0(. ) be the standard normal cumulative distribution function and (.) be the standard normal density function. Please write down the Probit model to describe the probability of graduating in five years in terms of hsGPA, SAT and study. Please write down the partial effect of study on P(grad = 1|hsGPA, SAT, study). %3D (ii) If we use a Linear Probability Model instead, write down the model that you'll estimate. What limitations does this model have? (iii) Suppose that, using data on 420 student-athletes, the following logit model is obtained: P(grad = 1|hsGPA, SAT, study) = A(-1.17+ .24hsGPA+ .00058SAT + .073study) where A(z) = exp(z)[1+ exp(z)]. Please give the expressions for P(grad = 1|hsGPA,SAT,study) P(grad = 0|hsGPA,SAT,study) P(grad = 1|hsGPA,SAT,study) log 1-P(grad = 1|hsGPA,SAT,study) and Please show your work as detailed as possible.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![Let grad be a dummy variable for whether a student-athlete at a large university graduates in five
years. Let hsGPA and SAT be high school grade point average and SAT score, respectively. Let study
be the number of hours spent per week in an organized study hall.
i) Let 0( . ) be the standard normal cumulative distribution function and (· ) be the standard
normal density function. Please write down the Probit model to describe the probability of
graduating in five years in terms of hsGPA, SAT and study. Please write down the partial effect of
study on P(grad = 1|hsGPA, SAT, study).
(ii) If we use a Linear Probability Model instead, write down the model that you'll estimate. What
limitations does this model have?
(iii) Suppose that, using data on 420 student-athletes, the following logit model is obtained:
P(grad = 1|hsGPA, SAT, study) =A(-1.17+ .24hsGPA+ .00058SAT+ .073study)
where A(z) = exp(z)[1+ exp(z)]. Please give the expressions for
P(grad = 1|hsGPA,SAT,study)
P(grad = 0|hsGPA,SAT,study)
P(grad = 1|hsGPA,SAT,study)
log
1-P(grad = 1|hsGPA,SAT,study)'
%3D
and
Please show your work as detailed as possible.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F65ef8c55-31cc-43a7-9725-b632461ed4ff%2F38602c31-2bb1-40d9-b92a-e79143f9bedd%2Fk2xm5eh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let grad be a dummy variable for whether a student-athlete at a large university graduates in five
years. Let hsGPA and SAT be high school grade point average and SAT score, respectively. Let study
be the number of hours spent per week in an organized study hall.
i) Let 0( . ) be the standard normal cumulative distribution function and (· ) be the standard
normal density function. Please write down the Probit model to describe the probability of
graduating in five years in terms of hsGPA, SAT and study. Please write down the partial effect of
study on P(grad = 1|hsGPA, SAT, study).
(ii) If we use a Linear Probability Model instead, write down the model that you'll estimate. What
limitations does this model have?
(iii) Suppose that, using data on 420 student-athletes, the following logit model is obtained:
P(grad = 1|hsGPA, SAT, study) =A(-1.17+ .24hsGPA+ .00058SAT+ .073study)
where A(z) = exp(z)[1+ exp(z)]. Please give the expressions for
P(grad = 1|hsGPA,SAT,study)
P(grad = 0|hsGPA,SAT,study)
P(grad = 1|hsGPA,SAT,study)
log
1-P(grad = 1|hsGPA,SAT,study)'
%3D
and
Please show your work as detailed as possible.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
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
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
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
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
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
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman