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Questions and Answers
Which assumption states that the regression model is linear in parameter?
Which assumption states that the regression model is linear in parameter?
What does Assumption 2 imply about the relationship between the explanatory variable and the disturbance term?
What does Assumption 2 imply about the relationship between the explanatory variable and the disturbance term?
Which property of OLS estimators ensures they have minimum variance among linear estimators?
Which property of OLS estimators ensures they have minimum variance among linear estimators?
Which assumption ensures that the variance of error terms is constant in the linear regression model?
Which assumption ensures that the variance of error terms is constant in the linear regression model?
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What is the main implication of Assumption 6 in the classical linear regression model?
What is the main implication of Assumption 6 in the classical linear regression model?
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What distribution do the error terms follow according to Assumption 7?
What distribution do the error terms follow according to Assumption 7?
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Which property indicates that OLS estimators are efficient?
Which property indicates that OLS estimators are efficient?
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Why is it important that the explanatory variable is non-stochastic as stated in Assumption 2?
Why is it important that the explanatory variable is non-stochastic as stated in Assumption 2?
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Flashcards
Classical Linear Regression Model (CLRM)
Classical Linear Regression Model (CLRM)
A statistical model that assesses relationships between a dependent variable and one or more independent variables assuming linearity.
Assumption 1: Linearity in Parameters
Assumption 1: Linearity in Parameters
The regression model must be linear in its parameters, meaning parameters are combined linearly to form the equation.
Assumption 2: No Correlation with Disturbances
Assumption 2: No Correlation with Disturbances
The explanatory variable cannot be correlated with the disturbance term and must be non-stochastic.
Assumption 3: Mean of Disturbances
Assumption 3: Mean of Disturbances
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Assumption 4: Homoscedasticity
Assumption 4: Homoscedasticity
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Assumption 5: No Correlation Between Errors
Assumption 5: No Correlation Between Errors
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Gauss-Markov Theorem
Gauss-Markov Theorem
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Normal Distribution of Errors
Normal Distribution of Errors
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Study Notes
Classical Linear Regression Model (CLRM)
- The CLRM model is a linear relationship between variables
- Assumption 1: The model is linear in parameters (e.g., Y₁ = B₁ + B₂X₁ + Uᵢ)
- Assumption 2: Explanatory variables (X) are uncorrelated with the error term (U) and non-stochastic
- Assumption 3: The expected value of the error term (U) is zero, given the explanatory variable (X), meaning E(U | X) = 0
- Assumption 4: The variance of the error term (U) is constant across all observations (homoscedasticity), var(Uᵢ) = σ²
- Assumption 5: There's no correlation between error terms for different observations, cov(Uᵢ, Uⱼ) = 0 for i ≠ j
- Assumption 6: The regression model is correctly specified
- Assumption 7: Error terms follow a normal distribution (Uᵢ ~ N(0, σ²))
Properties of OLS Estimators
- Gauss-Markov Theorem: OLS estimators have minimum variance in the class of linear unbiased estimators (BLUE)
- Property 1: OLS estimators (b₁ and b₂) are linear functions of the dependent variable (Y)
- Property 2: OLS estimators are unbiased; E(b₁) = B₁ and E(b₂) = B₂
- Property 3: The OLS estimator of the error variance (σ²) is unbiased, E(σ²) = σ²
- Property 4: OLS estimators are efficient; their variances are smaller than any other linear unbiased estimator for B₁ and B₂
- Sampling distributions of b₁ and b₂ are normal if the error terms are normally distributed (b₁ ~ N(B₁, σ²_b₁), b₂ ~ N(B₂, σ²_b₂))
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Description
Test your knowledge on the Classical Linear Regression Model (CLRM) and its assumptions. This quiz covers key concepts including the properties of OLS estimators and the Gauss-Markov theorem. Challenge yourself to see how well you understand these foundational topics in statistics and econometrics.
