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 b3. iv. R². b. Interpret each of the estimates b₂, b3, and b4. c. Compute a 95% interval estimate for ß4.What does this interval tell you? d. Are each of the coefficient estimates significant at a 5% level? Why?

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.2: The Least Square Line
Problem 7E
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Please answer 5.3 a-e. Thank you!
-U-NWS
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) + B3NK + B4AGE + e
This model was estimated using 1200 observations from London. An incomplete version of this output
is provided in Table 5.6.
In(TOTEXP)
NK
AGE
TABLE 5.6
Dependent Variable: WALC
Included observations: 1200
Variable
C
Output for Exercise 5.3
R-squared
S.E. of regression
Sum squared resid
Coefficient
1.4515
2.7648
-0.1503
46221.62
Std. Error
2.2019
ii. The standard error for b₂.
iii. The estimate b3.
iv. R2.
0.3695
0.0235
labol noiseenga olqislum erit 5.8 Exercises 235
a. Fill in the following blank spaces that appear in this table.
i. The t-statistic for b₁.
t-Statistic
EM2000 5.7103
-3.9376
-6.4019
Mean dependent var
S.D. dependent var bon fald
v. 6.
b. Interpret each of the estimates b2, b3, and b4.
c. Compute a 95% interval estimate for ß4. What does this interval tell you?
d. Are each of the coefficient estimates significant at a 5% level? Why?
Prob.
0.5099
0.0000
0.0001
0.0000
6.19434
6.39547
most
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) + B3NK + B4AGE + B,AGE2 + 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 b3, b4, and bg.
a. 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.
b. Find a point estimate and a 95% interval estimate for the 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).
normally distributed,
Transcribed Image Text:-U-NWS 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) + B3NK + B4AGE + e This model was estimated using 1200 observations from London. An incomplete version of this output is provided in Table 5.6. In(TOTEXP) NK AGE TABLE 5.6 Dependent Variable: WALC Included observations: 1200 Variable C Output for Exercise 5.3 R-squared S.E. of regression Sum squared resid Coefficient 1.4515 2.7648 -0.1503 46221.62 Std. Error 2.2019 ii. The standard error for b₂. iii. The estimate b3. iv. R2. 0.3695 0.0235 labol noiseenga olqislum erit 5.8 Exercises 235 a. Fill in the following blank spaces that appear in this table. i. The t-statistic for b₁. t-Statistic EM2000 5.7103 -3.9376 -6.4019 Mean dependent var S.D. dependent var bon fald v. 6. b. Interpret each of the estimates b2, b3, and b4. c. Compute a 95% interval estimate for ß4. What does this interval tell you? d. Are each of the coefficient estimates significant at a 5% level? Why? Prob. 0.5099 0.0000 0.0001 0.0000 6.19434 6.39547 most 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) + B3NK + B4AGE + B,AGE2 + 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 b3, b4, and bg. a. 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. b. Find a point estimate and a 95% interval estimate for the 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). normally distributed,
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