d. Are each of the coefficient estimates significant at a 5% level? Why? e. Test the hypothesis that the addition of an extra child decreases the mean budget share of alcohol. by 2 percentage points against the alternative that the decrease is not equal to 2 percentage points. Use a 5% significance level.
d. Are each of the coefficient estimates significant at a 5% level? Why? e. Test the hypothesis that the addition of an extra child decreases the mean budget share of alcohol. by 2 percentage points against the alternative that the decrease is not equal to 2 percentage points. Use a 5% significance level.
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
Please answer 5.3 d and e
![2:01
--WS
5.3 Consider the following model that relates the percentage of a household's budget spent on alcohol
WALC to total expenditure TOTEXP, age of the household head AGE, and the number of children in
the household NK.
WALC=B₁ + B₂ In(TOTEXP) + B₂NK + BAGE+e
This model was estimated using 1200 observations from London. An incomplete version of this output
is provided in Table 5.6.
Output for Exercise 5.3
TABLE 5.6
Dependent Variable: WALC
Included observations: 1200
Variable
C
In(TOTEXP)
NK
AGE
R-squared
S.E. of regression
Sum squared resid
Coefficient
1.4515
2.7648
-0.1503
46221.62
Std. Error
2.2019
0.3695
0.0235
Jabolt noissgol 5.8 Ex
a. Fill in the following blank spaces that appear in this table.
i. The t-statistic for b₁.
ii. The standard error for b₂.
iii. The estimate by.
iv. R².
t-Statistic
ATSIOO
X
EMC 5.7103
-3.9376
-6.4019
Mean dependent var
allol od tod 6.19434
S.D. dependent varmabes (xl) 6.39547
114142
Prob.
0.5099
0.0000
0.0001
0.0000
V. 8.
b. Interpret each of the estimates b₂, b3, and b₁.
c. Compute a 95% interval estimate for B₁. What does this interval tell you?
d. Are each of the coefficient estimates significant at a 5% level? Why?
e. Test the hypothesis that the addition of an extra child decreases the mean budget share of alcohol
by 2 percentage points against the alternative that the decrease is not equal to 2 percentage points.
Use a 5% significance level.
5.4 Consider the following model that relates the percentage of a household's budget spent on alcohol,
WALC, to total expenditure TOTEXP, age of the household head AGE, and the number of children in
the household NK.
WALC=B₁ + B₂ In(TOTEXP) + B,NK + BAGE+BAGE² +e
Some output from estimating this model using 1200 observations from London is provided in Table 5.7.
The covariance matrix relates to the coefficients b, b, and b.
2. Find a point estimate and a 95% interval estimate for the change in the mean budget percentage
share for alcohol when a household has an extra child.
a marginal effect of AGE on the mean budget
c. Find a point estimate and a 95% interval estimate for the age at which the mean budget percentage
percentage share for alcohol when (i) AGE = 25, (ii) AGE = 50, and (iii) AGE= 75.
share for alcohol is at a minimum.
d. Summarize what you have discovered from the point and interval estimates in (a), (b), and (c).
ally distributed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6b1ec9e1-71c5-41a7-88e5-1ec0b0e62692%2Fc3e9dc04-b2f6-490f-b32e-7ae8efe2d8be%2Fuaf5f7c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2:01
--WS
5.3 Consider the following model that relates the percentage of a household's budget spent on alcohol
WALC to total expenditure TOTEXP, age of the household head AGE, and the number of children in
the household NK.
WALC=B₁ + B₂ In(TOTEXP) + B₂NK + BAGE+e
This model was estimated using 1200 observations from London. An incomplete version of this output
is provided in Table 5.6.
Output for Exercise 5.3
TABLE 5.6
Dependent Variable: WALC
Included observations: 1200
Variable
C
In(TOTEXP)
NK
AGE
R-squared
S.E. of regression
Sum squared resid
Coefficient
1.4515
2.7648
-0.1503
46221.62
Std. Error
2.2019
0.3695
0.0235
Jabolt noissgol 5.8 Ex
a. Fill in the following blank spaces that appear in this table.
i. The t-statistic for b₁.
ii. The standard error for b₂.
iii. The estimate by.
iv. R².
t-Statistic
ATSIOO
X
EMC 5.7103
-3.9376
-6.4019
Mean dependent var
allol od tod 6.19434
S.D. dependent varmabes (xl) 6.39547
114142
Prob.
0.5099
0.0000
0.0001
0.0000
V. 8.
b. Interpret each of the estimates b₂, b3, and b₁.
c. Compute a 95% interval estimate for B₁. What does this interval tell you?
d. Are each of the coefficient estimates significant at a 5% level? Why?
e. Test the hypothesis that the addition of an extra child decreases the mean budget share of alcohol
by 2 percentage points against the alternative that the decrease is not equal to 2 percentage points.
Use a 5% significance level.
5.4 Consider the following model that relates the percentage of a household's budget spent on alcohol,
WALC, to total expenditure TOTEXP, age of the household head AGE, and the number of children in
the household NK.
WALC=B₁ + B₂ In(TOTEXP) + B,NK + BAGE+BAGE² +e
Some output from estimating this model using 1200 observations from London is provided in Table 5.7.
The covariance matrix relates to the coefficients b, b, and b.
2. Find a point estimate and a 95% interval estimate for the change in the mean budget percentage
share for alcohol when a household has an extra child.
a marginal effect of AGE on the mean budget
c. Find a point estimate and a 95% interval estimate for the age at which the mean budget percentage
percentage share for alcohol when (i) AGE = 25, (ii) AGE = 50, and (iii) AGE= 75.
share for alcohol is at a minimum.
d. Summarize what you have discovered from the point and interval estimates in (a), (b), and (c).
ally distributed.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
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 3 steps
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![MATLAB: An Introduction with Applications](https://www.bartleby.com/isbn_cover_images/9781119256830/9781119256830_smallCoverImage.gif)
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
![Probability and Statistics for Engineering and th…](https://www.bartleby.com/isbn_cover_images/9781305251809/9781305251809_smallCoverImage.gif)
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
![Statistics for The Behavioral Sciences (MindTap C…](https://www.bartleby.com/isbn_cover_images/9781305504912/9781305504912_smallCoverImage.gif)
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](https://www.bartleby.com/isbn_cover_images/9781119256830/9781119256830_smallCoverImage.gif)
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
![Probability and Statistics for Engineering and th…](https://www.bartleby.com/isbn_cover_images/9781305251809/9781305251809_smallCoverImage.gif)
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
![Statistics for The Behavioral Sciences (MindTap C…](https://www.bartleby.com/isbn_cover_images/9781305504912/9781305504912_smallCoverImage.gif)
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…](https://www.bartleby.com/isbn_cover_images/9780134683416/9780134683416_smallCoverImage.gif)
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
![The Basic Practice of Statistics](https://www.bartleby.com/isbn_cover_images/9781319042578/9781319042578_smallCoverImage.gif)
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](https://www.bartleby.com/isbn_cover_images/9781319013387/9781319013387_smallCoverImage.gif)
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman