4 marks, −1EconometricsLinear regression and OLSThe Gauss-Markov theorem and OLS propertiesModerateabout 2 min

DSE 2018 Question 20: Linear regression and OLS

Consider the model $y = \beta_0 + \beta_1 X_1 + \beta_2 X_2 + \epsilon$ , estimated using OLS. Which of the following will lead to a higher $\mathrm{Var}(\hat{\beta}_2)$ ? (i) Smaller sample size; (ii) Less variation in $X_2$ ; (iii) More variation in $\epsilon$ ; (iv) Higher correlation between $X_1$ and $X_2$ .

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Consider the model y = β₀ + β₁ X₁ + β₂ X₂ + ϵ, estimated using OLS. Which of the following will lead to a higher Var(β̂₂)? (i) Smaller sample size; (ii) Less variation in X₂; (iii) More variation in ϵ; (iv) Higher correlation between X₁ and X₂. (A) (i), (ii), (iii) and (iv) (B) (ii), (iii) and (iv) (C) (ii) and (iii) (D) (iii) and (iv)

Also written as: Consider the model y = beta_0 + beta_1 X_1 + beta_2 X_2 + epsilon, estimated using OLS. Which of the following will lead to a higher Var(beta_hat_2)? (i) Smaller sample size; (ii) Less variation in X_2; (iii) More variation in epsilon; (iv) Higher correlation between X_1 and X_2.

Linear regression and OLS has come up 74 times in 7 exams since 2008.

What this question tests

This question is on The Gauss-Markov theorem and OLS properties, part of Linear regression and OLS in Econometrics.

Why OLS is the best linear unbiased estimator, and what it needs.

TestStop has 6 past-paper questions on this subtopic.

Practise Linear regression and OLS More on The Gauss-Markov theorem and OLS properties

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Plain-text version

Linear regression and OLS has come up 74 times in 7 exams since 2008.

What this question tests

This question is on The Gauss-Markov theorem and OLS properties, part of Linear regression and OLS in Econometrics.

Why OLS is the best linear unbiased estimator, and what it needs.

TestStop has 6 past-paper questions on this subtopic.

Question from the DSE 2018 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.

DSE 2018 Question 20: Linear regression and OLS

Answer and worked solution

What this question tests

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DSE 2018 Question 20: Linear regression and OLS

Answer and worked solution

What this question tests

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