Problem 3 (25 points) We estimate the relationship between individual SAT score and several characteristics. The variable sat is the combined SAT score; hsize is size of the student's high school graduating class, in hundreds; hsizesq is a square of hsize female is a gender dummy variable equal to one for women, and zero otherwise; black is a race dummy variable equal to one for blacks, and zero otherwise; fem_black is an interaction (product) of female and black; in other words, it is equal to 1 for female black students and zero otherwise Here is the regression output: Source ss df MS Number of obs 4,036 F(5, 4030) 76.29 Model Residual 6795258.21 71792611.4 5 1359051.64 4,030 17814.5438 Prob > F 0.0000 R-squared 0.0865 Adj R-squared 0.0853 Total 78587869.6 4,035 19476.5476 Root MSE 133.47 sat Coefficient Std. err. t P>|t| [95% conf. interval] hsize hsizesq female black fem_black _cons 20.02221 3.894369 5.14 0.000 -2.282131 .5355272 -4.26 0.000 -46.42134 4.349489 -10.67 0.000 -168.2233 12.78395 -13.16 0.000 63.70131 18.29501 3.48 0.001 1027.107 6.406106 160.33 0.000 12.38709 27.65732 -3.33206 -1.232201 -54.94874 -37.89394 -193.2869 -143.1597 27.83299 99.56963 1014.547 1039.666 1) Is there strong evidence that hsizesq should be included in the model? How did you determine that? 2) Sketch the relationship between high school class and SAT scores on a graph. 3) Holding hsize fixed, what is the estimated difference in SAT score between nonblack females and nonblack males? How statistically significant is this estimated difference? Hint: consider what happens when black dummy is equal to zero. 4) What is the estimated difference in SAT score between nonblack males and black males? Test the null hypothesis that there is no difference between their scores, against the alternative that there is a difference. Hint: consider what happens when female dummy is equal to zero.
Problem 3 (25 points) We estimate the relationship between individual SAT score and several characteristics. The variable sat is the combined SAT score; hsize is size of the student's high school graduating class, in hundreds; hsizesq is a square of hsize female is a gender dummy variable equal to one for women, and zero otherwise; black is a race dummy variable equal to one for blacks, and zero otherwise; fem_black is an interaction (product) of female and black; in other words, it is equal to 1 for female black students and zero otherwise Here is the regression output: Source ss df MS Number of obs 4,036 F(5, 4030) 76.29 Model Residual 6795258.21 71792611.4 5 1359051.64 4,030 17814.5438 Prob > F 0.0000 R-squared 0.0865 Adj R-squared 0.0853 Total 78587869.6 4,035 19476.5476 Root MSE 133.47 sat Coefficient Std. err. t P>|t| [95% conf. interval] hsize hsizesq female black fem_black _cons 20.02221 3.894369 5.14 0.000 -2.282131 .5355272 -4.26 0.000 -46.42134 4.349489 -10.67 0.000 -168.2233 12.78395 -13.16 0.000 63.70131 18.29501 3.48 0.001 1027.107 6.406106 160.33 0.000 12.38709 27.65732 -3.33206 -1.232201 -54.94874 -37.89394 -193.2869 -143.1597 27.83299 99.56963 1014.547 1039.666 1) Is there strong evidence that hsizesq should be included in the model? How did you determine that? 2) Sketch the relationship between high school class and SAT scores on a graph. 3) Holding hsize fixed, what is the estimated difference in SAT score between nonblack females and nonblack males? How statistically significant is this estimated difference? Hint: consider what happens when black dummy is equal to zero. 4) What is the estimated difference in SAT score between nonblack males and black males? Test the null hypothesis that there is no difference between their scores, against the alternative that there is a difference. Hint: consider what happens when female dummy is equal to zero.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
![Problem 3 (25 points)
We estimate the relationship between individual SAT score and several characteristics.
The variable sat is the combined SAT score;
hsize is size of the student's high school graduating class, in hundreds;
hsizesq is a square of hsize
female is a gender dummy variable equal to one for women, and zero otherwise;
black is a race dummy variable equal to one for blacks, and zero otherwise;
fem_black is an interaction (product) of female and black; in other words, it is equal to 1 for
female black students and zero otherwise
Here is the regression output:
Source
ss
df
MS
Number of obs
4,036
F(5, 4030)
76.29
Model
Residual
6795258.21
71792611.4
5 1359051.64
4,030 17814.5438
Prob > F
0.0000
R-squared
0.0865
Adj R-squared
0.0853
Total
78587869.6
4,035 19476.5476
Root MSE
133.47
sat
Coefficient Std. err.
t
P>|t|
[95% conf. interval]
hsize
hsizesq
female
black
fem_black
_cons
20.02221 3.894369
5.14 0.000
-2.282131 .5355272 -4.26 0.000
-46.42134 4.349489 -10.67 0.000
-168.2233 12.78395 -13.16 0.000
63.70131 18.29501 3.48 0.001
1027.107 6.406106 160.33 0.000
12.38709
27.65732
-3.33206 -1.232201
-54.94874
-37.89394
-193.2869
-143.1597
27.83299
99.56963
1014.547
1039.666
1) Is there strong evidence that hsizesq should be included in the model? How did you
determine that?
2) Sketch the relationship between high school class and SAT scores on a graph.
3) Holding hsize fixed, what is the estimated difference in SAT score between nonblack
females and nonblack males? How statistically significant is this estimated difference?
Hint: consider what happens when black dummy is equal to zero.
4) What is the estimated difference in SAT score between nonblack males and black males?
Test the null hypothesis that there is no difference between their scores, against the
alternative that there is a difference.
Hint: consider what happens when female dummy is equal to zero.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0bd741cb-e18a-41d4-b913-544d1a64d4b0%2F70d21373-b9a4-437c-ade2-8bdd7f38b9cd%2Frm4vp2_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem 3 (25 points)
We estimate the relationship between individual SAT score and several characteristics.
The variable sat is the combined SAT score;
hsize is size of the student's high school graduating class, in hundreds;
hsizesq is a square of hsize
female is a gender dummy variable equal to one for women, and zero otherwise;
black is a race dummy variable equal to one for blacks, and zero otherwise;
fem_black is an interaction (product) of female and black; in other words, it is equal to 1 for
female black students and zero otherwise
Here is the regression output:
Source
ss
df
MS
Number of obs
4,036
F(5, 4030)
76.29
Model
Residual
6795258.21
71792611.4
5 1359051.64
4,030 17814.5438
Prob > F
0.0000
R-squared
0.0865
Adj R-squared
0.0853
Total
78587869.6
4,035 19476.5476
Root MSE
133.47
sat
Coefficient Std. err.
t
P>|t|
[95% conf. interval]
hsize
hsizesq
female
black
fem_black
_cons
20.02221 3.894369
5.14 0.000
-2.282131 .5355272 -4.26 0.000
-46.42134 4.349489 -10.67 0.000
-168.2233 12.78395 -13.16 0.000
63.70131 18.29501 3.48 0.001
1027.107 6.406106 160.33 0.000
12.38709
27.65732
-3.33206 -1.232201
-54.94874
-37.89394
-193.2869
-143.1597
27.83299
99.56963
1014.547
1039.666
1) Is there strong evidence that hsizesq should be included in the model? How did you
determine that?
2) Sketch the relationship between high school class and SAT scores on a graph.
3) Holding hsize fixed, what is the estimated difference in SAT score between nonblack
females and nonblack males? How statistically significant is this estimated difference?
Hint: consider what happens when black dummy is equal to zero.
4) What is the estimated difference in SAT score between nonblack males and black males?
Test the null hypothesis that there is no difference between their scores, against the
alternative that there is a difference.
Hint: consider what happens when female dummy is equal to zero.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
Engineering Economy (17th Edition)
Economics
ISBN:
9780134870069
Author:
William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:
PEARSON
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
Engineering Economy (17th Edition)
Economics
ISBN:
9780134870069
Author:
William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:
PEARSON
Principles of Economics (MindTap Course List)
Economics
ISBN:
9781305585126
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
Managerial Economics: A Problem Solving Approach
Economics
ISBN:
9781337106665
Author:
Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:
Cengage Learning
Managerial Economics & Business Strategy (Mcgraw-…
Economics
ISBN:
9781259290619
Author:
Michael Baye, Jeff Prince
Publisher:
McGraw-Hill Education