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S a. Fill in the following blank spaces that appear in this table. L. The f-statistic for b₁. ii. The standard error for b₂. iii. The estimate by. iv. R². b. Interpret each of the estimates by, by, and b. c. Compute a 95% interval estimate for p..What does this interval tell you? d. Are each of the coefficient estimates significant at a 5% level? Why? 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. 54 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 by, 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. b. Find a point estimate and a 95% interval estimate for the marginal effect of AGE on the mean budget percentage share for alcohol when (i) AGE=25, (ii) AGE= 50, and (iii) AGE = 75. c. Find a point estimate and a 95% interval estimate for the age at which the mean budget percentage share for alcohol is at a minimum. d. Summarize what you have discovered from the point and interval estimates in (a), (b), and (c). e. Let X represent all the observations on all the explanatory variables. If (e|X) is normally distributed, which of the above interval estimates are valid in finite samples? Which ones rely on a large sample approximation? t. If (elX) is not normally distributed, which of the above interval estimates are valid in finite samples? Which ones rely on a large sample approximation?

S a. Fill in the following blank spaces that appear in this table. L. The f-statistic for b₁. ii. The standard error for b₂. iii. The estimate by. iv. R². b. Interpret each of the estimates by, by, and b. c. Compute a 95% interval estimate for p..What does this interval tell you? d. Are each of the coefficient estimates significant at a 5% level? Why? 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. 54 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 by, 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. b. Find a point estimate and a 95% interval estimate for the marginal effect of AGE on the mean budget percentage share for alcohol when (i) AGE=25, (ii) AGE= 50, and (iii) AGE = 75. c. Find a point estimate and a 95% interval estimate for the age at which the mean budget percentage share for alcohol is at a minimum. d. Summarize what you have discovered from the point and interval estimates in (a), (b), and (c). e. Let X represent all the observations on all the explanatory variables. If (e|X) is normally distributed, which of the above interval estimates are valid in finite samples? Which ones rely on a large sample approximation? t. If (elX) is not normally distributed, which of the above interval estimates are valid in finite samples? Which ones rely on a large sample approximation?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Please answer 5.4 d-f
Certainly! Here's the transcribed text and an explanation suitable for an educational website: --- ### Exercise: Economic Model Analysis **Tasks:** 1. Fill in the following blank spaces that appear in the table: - i. The t-statistic for \( b_1 \). - ii. The standard error for \( b_2 \). - iii. The estimate \( b_3 \). - iv. \( R^2 \). 2. **Interpretation:** - Interpret each of the estimates \( b_2 \), \( b_3 \), and \( b_4 \). 3. **Interval Estimate:** - Compute a 95% interval estimate for \( b_1 \). What does this interval tell you? 4. **Significance Testing:** - Are each of the coefficient estimates significant at a 5% level? Why? 5. **Hypothesis Testing:** - 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. ### Economic Model: 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 \( NK \): \[ WALC = \beta_1 + \beta_2 \ln(TOTEXP) + \beta_3 NK + \beta_4 AGE + \beta_5 AGE^2 + e \] Some output from estimating this model using 1200 observations from London is provided in Table 5.7. The covariance matrix relates to the coefficients \( b_3 \), \( b_4 \), and \( b_5 \). ### Further Analysis: d. 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. e. Find a point estimate and a 95% interval estimate for the marginal effect of \( AGE \) on the mean budget percentage share for alcohol when: - i. \( AGE = 25 \) - ii. \( AGE = 50 \) - iii. \( AGE = 75 \) f. Summarize what you have discovered from
Transcribed Image Text:Certainly! Here's the transcribed text and an explanation suitable for an educational website: --- ### Exercise: Economic Model Analysis **Tasks:** 1. Fill in the following blank spaces that appear in the table: - i. The t-statistic for \( b_1 \). - ii. The standard error for \( b_2 \). - iii. The estimate \( b_3 \). - iv. \( R^2 \). 2. **Interpretation:** - Interpret each of the estimates \( b_2 \), \( b_3 \), and \( b_4 \). 3. **Interval Estimate:** - Compute a 95% interval estimate for \( b_1 \). What does this interval tell you? 4. **Significance Testing:** - Are each of the coefficient estimates significant at a 5% level? Why? 5. **Hypothesis Testing:** - 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. ### Economic Model: 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 \( NK \): \[ WALC = \beta_1 + \beta_2 \ln(TOTEXP) + \beta_3 NK + \beta_4 AGE + \beta_5 AGE^2 + e \] Some output from estimating this model using 1200 observations from London is provided in Table 5.7. The covariance matrix relates to the coefficients \( b_3 \), \( b_4 \), and \( b_5 \). ### Further Analysis: d. 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. e. Find a point estimate and a 95% interval estimate for the marginal effect of \( AGE \) on the mean budget percentage share for alcohol when: - i. \( AGE = 25 \) - ii. \( AGE = 50 \) - iii. \( AGE = 75 \) f. Summarize what you have discovered from
**The Multiple Regression Model** ### Table 5.7: Output for Exercise 5.4 | Variable | Coefficient | |-----------------|-------------| | \( C \) | 8.149 | | \( \ln(TOTEXP) \) | 2.884 | | \( NK \) | -1.217 | | \( AGE \) | -0.5699 | | \( AGE^2 \) | 0.005515 | #### Covariance Matrix | | \( NK \) | \( AGE \) | \( AGE^2 \) | |----------|-------------|-------------|---------------| | \( NK \) | 0.1462 | -0.01774 | 0.0002347 | | \( AGE \)| -0.01774 | 0.03204 | -0.0004138 | | \( AGE^2\) | 0.0002347 | -0.0004138 | 0.00005438 | ### Explanations #### Exercise 5.5 For each of the following two time-series regression models, and assuming \( \text{MR1-MR6} \) hold, find \( \text{var}(b_k) \) and examine whether the least squares estimator is consistent by checking whether \( \lim_{T \to \infty} \text{var}(b_k)/T = 0 \). a. \( y_t = \beta_1 + \beta_2 t + e_t, t = 1, 2, \ldots, T. \) - Note that \( x = (1, 2, \ldots, T). \) - \(\sum_{t=1}^{T} t^2 - \left( \sum_{t=1}^{T} t \right)^2 / T = \sum_{t=1}^{T} t^2 - (\sum_{t=1}^{T} t)^2 / T\) b. \( y_t = \beta_1 + \beta_2 x_t + e_t, x_t = T(t+1)/2 + T(t+1)(2T+1)/6. \) - \( y_t = \beta_1 + \beta_2
Transcribed Image Text:**The Multiple Regression Model** ### Table 5.7: Output for Exercise 5.4 | Variable | Coefficient | |-----------------|-------------| | \( C \) | 8.149 | | \( \ln(TOTEXP) \) | 2.884 | | \( NK \) | -1.217 | | \( AGE \) | -0.5699 | | \( AGE^2 \) | 0.005515 | #### Covariance Matrix | | \( NK \) | \( AGE \) | \( AGE^2 \) | |----------|-------------|-------------|---------------| | \( NK \) | 0.1462 | -0.01774 | 0.0002347 | | \( AGE \)| -0.01774 | 0.03204 | -0.0004138 | | \( AGE^2\) | 0.0002347 | -0.0004138 | 0.00005438 | ### Explanations #### Exercise 5.5 For each of the following two time-series regression models, and assuming \( \text{MR1-MR6} \) hold, find \( \text{var}(b_k) \) and examine whether the least squares estimator is consistent by checking whether \( \lim_{T \to \infty} \text{var}(b_k)/T = 0 \). a. \( y_t = \beta_1 + \beta_2 t + e_t, t = 1, 2, \ldots, T. \) - Note that \( x = (1, 2, \ldots, T). \) - \(\sum_{t=1}^{T} t^2 - \left( \sum_{t=1}^{T} t \right)^2 / T = \sum_{t=1}^{T} t^2 - (\sum_{t=1}^{T} t)^2 / T\) b. \( y_t = \beta_1 + \beta_2 x_t + e_t, x_t = T(t+1)/2 + T(t+1)(2T+1)/6. \) - \( y_t = \beta_1 + \beta_2
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