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Questions › DSE › DSE 2021 › Q44
4 marks, −1Econometrics › Linear regression and OLS › The regression model and the OLS estimatorModerateabout 2 min

DSE 2021 Question 44: Linear regression and OLS

Suppose we run the OLS regression Yi=α+βXi+ϵiY_i = \alpha + \beta X_i + \epsilon_iYi​=α+βXi​+ϵi​, where notations have their usual meaning. After this we get an estimate Y^i=α^+β^Xi\hat{Y}_i = \hat{\alpha} + \hat{\beta}X_iY^i​=α^+β^​Xi​. Now we regress (OLS) YiY_iYi​ on Y^i\hat{Y}_iY^i​. The estimated coefficient of Y^i\hat{Y}_iY^i​ is γ^\hat{\gamma}γ^​. Which of the following is correct?

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Suppose we run the OLS regression Yᵢ = α + β Xᵢ + ϵᵢ, where notations have their usual meaning. After this we get an estimate Ŷᵢ = α̂ + β̂Xᵢ. Now we regress (OLS) Yᵢ on Ŷᵢ. The estimated coefficient of Ŷᵢ is γ̂. Which of the following is correct? (A) γ̂ = α̂ (B) γ̂ = β̂ (C) γ̂ = 0 (D) γ̂ = 1

Also written as: Suppose we run the OLS regression Y_i = alpha + beta X_i + epsilon_i, where notations have their usual meaning. After this we get an estimate Y_hat_i = alpha_hat + beta_hatX_i. Now we regress (OLS) Y_i on Y_hat_i. The estimated coefficient of Y_hat_i is gamma_hat. Which of the following is correct?

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

What this question tests

This question is on The regression model and the OLS estimator, part of Linear regression and OLS in Econometrics.

What a linear regression model is and how ordinary least squares picks the fitted line.

TestStop has 16 past-paper questions on this subtopic.

Practise Linear regression and OLSMore on The regression model and the OLS estimator

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