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?
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?
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
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Please answer 5.3 a-e. Thank you!
![**Exercise 5.3: Analyzing Household Budget on Alcohol Expenditure**
**Introduction:**
Consider the following model that relates the percentage of a household’s budget spent on alcohol, \( WALC \), to total expenditure \( TOTEXP \), the age of the household head \( AGE \), and the number of children in the household \( NK \).
\[ WALC = \beta_1 + \beta_2 \ln(TOTEXP) + \beta_3 NK + \beta_4 AGE + e \]
This model was estimated using 1200 observations from London. An incomplete version of this output is provided in Table 5.6.
**Table 5.6: Output for Exercise 5.3**
| Variable | Coefficient | Std. Error | t-Statistic | Prob. |
|----------------|-------------|------------|-------------|--------|
| C | 1.4515 | 2.2019 | | 0.5099 |
| \(\ln(TOTEXP)\)| 2.7648 | | 5.7103 | 0.0000 |
| NK | -0.1503 | 0.3695 | -3.9376 | 0.0000 |
| AGE | | 0.0235 | -6.4019 | 0.0000 |
- **R-squared:** 0.1633
- **S.E. of regression:** 6.39547
- **Sum squared resid:** 46221.62
- **Mean dependent var:** 6.1943
**Tasks:**
a. Fill in the following blank spaces that appear in this table.
- i. The t-statistic for \(\beta_1\).
- ii. The standard error for \(\beta_2\).
- iii. The estimate \(\beta_4\).
- iv. \( R^2 \).
b. Interpret each of the estimates \(\beta_2\), \(\beta_3\), and \(\beta_4\).
c. Compute a 95% interval estimate for \(\beta_4\). 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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6b1ec9e1-71c5-41a7-88e5-1ec0b0e62692%2F0ecb46b5-68fe-40f3-91ed-619d15381e49%2Femlsxwa_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Exercise 5.3: Analyzing Household Budget on Alcohol Expenditure**
**Introduction:**
Consider the following model that relates the percentage of a household’s budget spent on alcohol, \( WALC \), to total expenditure \( TOTEXP \), the age of the household head \( AGE \), and the number of children in the household \( NK \).
\[ WALC = \beta_1 + \beta_2 \ln(TOTEXP) + \beta_3 NK + \beta_4 AGE + e \]
This model was estimated using 1200 observations from London. An incomplete version of this output is provided in Table 5.6.
**Table 5.6: Output for Exercise 5.3**
| Variable | Coefficient | Std. Error | t-Statistic | Prob. |
|----------------|-------------|------------|-------------|--------|
| C | 1.4515 | 2.2019 | | 0.5099 |
| \(\ln(TOTEXP)\)| 2.7648 | | 5.7103 | 0.0000 |
| NK | -0.1503 | 0.3695 | -3.9376 | 0.0000 |
| AGE | | 0.0235 | -6.4019 | 0.0000 |
- **R-squared:** 0.1633
- **S.E. of regression:** 6.39547
- **Sum squared resid:** 46221.62
- **Mean dependent var:** 6.1943
**Tasks:**
a. Fill in the following blank spaces that appear in this table.
- i. The t-statistic for \(\beta_1\).
- ii. The standard error for \(\beta_2\).
- iii. The estimate \(\beta_4\).
- iv. \( R^2 \).
b. Interpret each of the estimates \(\beta_2\), \(\beta_3\), and \(\beta_4\).
c. Compute a 95% interval estimate for \(\beta_4\). 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
Expert Solution
Step 1
Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts. In case you require the unanswered parts also, kindly re-post that parts separately.
a.
i)
t statistic for b1:
ii)
Standard error for b2:
iii)
Estimate b3:
iv)
Given that
SSE=46221.62.
Therefore,
v)
Here, N=sample size=1200, Number of independent variables=3
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Solved in 3 steps
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