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Questions and Answers
In a byregion with 12 zones, where inhabitants live in one zone and work in another, how many unique combinations of residence and workplace are possible?
In a byregion with 12 zones, where inhabitants live in one zone and work in another, how many unique combinations of residence and workplace are possible?
- 132
- 144 (correct)
- 156
- 72
Assuming Eij are independent and normally distributed with a mean of zero and variance of 50, and β = 0.2, the expected utility of traveling from zone i to zone j is always positive.
Assuming Eij are independent and normally distributed with a mean of zero and variance of 50, and β = 0.2, the expected utility of traveling from zone i to zone j is always positive.
False (B)
Given $e = \epsilon_{11} - \epsilon_{12}$, where (\epsilon_{11}) and (\epsilon_{12}) are independent and normally distributed with a mean of zero and variance of 50, what is the variance of e?
Given $e = \epsilon_{11} - \epsilon_{12}$, where (\epsilon_{11}) and (\epsilon_{12}) are independent and normally distributed with a mean of zero and variance of 50, what is the variance of e?
100
If a person prefers to live in zone 2 and work in zone 1 over living and working in zone 1, it implies that the utility of living and working in zone 2 is ______ than living and working in zone 1.
If a person prefers to live in zone 2 and work in zone 1 over living and working in zone 1, it implies that the utility of living and working in zone 2 is ______ than living and working in zone 1.
Given Cov[U, V] = E[U•V] – E[U]•E[V], which expression is equivalent to Cov[X + Y, W]?
Given Cov[U, V] = E[U•V] – E[U]•E[V], which expression is equivalent to Cov[X + Y, W]?
If X, Y, and Z are independent random variables, then Cov[X + Y, Z + Y] = Var[Y].
If X, Y, and Z are independent random variables, then Cov[X + Y, Z + Y] = Var[Y].
Given that (\epsilon_{ij}) are independent with a mean of zero and constant variance (\sigma^2 \ne 0), and (\tilde{\epsilon}{ij} = \epsilon{ij} + \epsilon_{ji} - \epsilon_{ii} - \epsilon_{jj}), what is the expected value of (\tilde{\epsilon}_{ij}) when $i \ne j$?
Given that (\epsilon_{ij}) are independent with a mean of zero and constant variance (\sigma^2 \ne 0), and (\tilde{\epsilon}{ij} = \epsilon{ij} + \epsilon_{ji} - \epsilon_{ii} - \epsilon_{jj}), what is the expected value of (\tilde{\epsilon}_{ij}) when $i \ne j$?
If the choice of workplace and residence are independent, the cell values in the table would represent the ______ frequencies based on marginal totals.
If the choice of workplace and residence are independent, the cell values in the table would represent the ______ frequencies based on marginal totals.
Match the following terms with their descriptions regarding the regression analysis in the text:
Match the following terms with their descriptions regarding the regression analysis in the text:
In the context of analyzing travel behavior, dij + dji represents:
In the context of analyzing travel behavior, dij + dji represents:
Flashcards
Combinations of Residence/Workplace
Combinations of Residence/Workplace
The number of different combinations of where people live and work, given 12 zones in a city region.
Expected Utility of Travel
Expected Utility of Travel
The expected utility of traveling from zone i to zone j, given a utility function Uij = -βdij + εij, where εij is normally distributed with mean zero and variance 50, and β = 0.2.
Define ε
Define ε
A variable ε defined as ε = ε11 - ε12, where ε11 and ε12 are independent and normally distributed with mean zero and variance 50.
Probability of Preference
Probability of Preference
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Cov[X + Y, W]
Cov[X + Y, W]
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Cov[X + Y, Z + Y]
Cov[X + Y, Z + Y]
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Characteristics of εij
Characteristics of εij
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Marginal Totals Interpretation
Marginal Totals Interpretation
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Conclusion of Chi-squared test
Conclusion of Chi-squared test
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Regression Comparison Conclusion
Regression Comparison Conclusion
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Study Notes
- Study notes from the provided text relating to statistics for economists:
Task 1
- A byregion is composed of 12 distinct zones, with inhabitants mainly residing in one zone and working in another.
- There exist 144 (12*12) possible combinations of residence and workplace.
- Zone 1 is considered the city center, with other zones ordered by their distance from it.
- There are 66 combinations where the workplace is nearer to the city center than the residence.
- dij represents the travel distance between zone i and zone j.
- The utility of traveling from zone i to zone j is given by Uij = -β dij + Eij.
- Eij is assumed to be independently and normally distributed with an expected value of zero and a variance of 50.
- The parameter β is set to 0.2.
- The expected utility of traveling from i to j is E[-βdij + €ij] = -βdij, with a negative sign indicating utility decreases with longer travel distances.
- ∈ is defined as ∈ = €11 - €12.
- ∈ is normally distributed with an expectation of 0 and a variance of 100.
- A person prefers living in zone 2 and working in zone 1 if U11 < U12; the probability of this preference is 15.87%.
Task 2
- This task requires technical skill.
- X, Y, Z, and W are random variables.
- Covariance: Cov[X + Y, W] = Cov[X, W] + Cov[Y, W].
- If X, Y, and Z are independent, Cov[X + Y, Z + Y] = Var[Y].
- For all pairs (i, j) where i and j range from 1 to 12, Eij are independent with an expected value of zero and constant variance σ² ≠ 0.
- *čij *is defined as eij + eji - eii - ejj.
- The expected value of čij when i ≠ jis 0, and its variance is 4σ².
- The covariance between €12 and €13 is σ² ≠ 0, meaning they are dependent variables.
Task 3
- A byregion contains four zones.
- A table shows the number of people living in one zone and working in another.
- The marginal totals represent the number of workers residing in each zone (20,000; 40,000; 60,000; 80,000) and the number of jobs in each zone (100,000; 40,000; 40,000; 20,000).
- Zone 1 is characterized as the city center, with more jobs (100,000) than residents (20,000),
- If workplace choice is independent of residence, an expected table can be computed.
- A chi-squared test is used to assess the independence of workplace and residence choices, resulting in a clear rejection of independence due to a significant test statistic of 1108.34, which is much higher than the critical value of 16.9.
Task 4
- A byregion has 12 zones.
- dij is the travel distance from zone i to zone j.
- Tij represents the number of employed individuals living in zone i and working in zone j.
- Tij = Ai Bje-Bdij+eij, where β is constant, Ai and Bj are constants for all i and j, and €ij are independently normally distributed with N[0, σ²].
- The equation ln(TijTji/TiiTjj) = -β(dij + dji) + (Eij + Eji – Eii - Ejj) holds true.
- Fij = -β(dij + dji) + (Eij + Eji — Eii - Ejj).
- dij + dji can be interpreted as the total travel distance to and from work and may not be equal due to one-way streets.
- All combinations where i > j amount to 66.
- Residual variance is constant.
- Ordinary Least Squares (OLS) cannot be used to estimate β, as not all residuals are independent.
- Generalized Least Squares (GLS) is used, removing dependence in residuals.
- The travel distance clearly matters.
- The results indicate that selecting a short commute is more important for a specific population group.
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