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.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
icon
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.
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
steps

Step by step

Solved in 3 steps

Blurred answer
Recommended textbooks for you
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Glencoe Algebra 1, Student Edition, 9780079039897…
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
College Algebra
College Algebra
Algebra
ISBN:
9781938168383
Author:
Jay Abramson
Publisher:
OpenStax
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt