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Questions › DSE › DSE 2012 › Q31
2 marksEconometrics › Linear regression and OLS › The regression model and the OLS estimatorHardabout 4 min

DSE 2012 Question 31: Linear regression and OLS

Consider the following model, estimated using OLS Yi=βXi+εi; i=1,2,...,nY_{i}=\beta X_{i}+\varepsilon_{i};\ i=1,2,...,nYi​=βXi​+εi​; i=1,2,...,n where there is no intercept, and Var(εi)=σ2Var(\varepsilon_{i})=\sigma^{2}Var(εi​)=σ2. Which of the following statements is not true?

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Consider the following model, estimated using OLS Yᵢ=β Xᵢ+εᵢ; i=1,2,...,n where there is no intercept, and Var(εᵢ)=σ². Which of the following statements is not true? (A) The R² from this regression can be large even if X and Y have low correlation. (B) The least squares residuals need not sum to zero. (C) The mean square error is given by Σ(Yᵢ-Ŷ)²/(n-1). (D) The least squares estimator of the slope coefficient is given by: (nΣ XᵢYᵢ-Σ XᵢΣ Yᵢ)/(nΣ Xᵢ²-(Σ Xᵢ)²)

Also written as: Consider the following model, estimated using OLS Y_i=beta X_i+epsilon_i; i=1,2,...,n where there is no intercept, and Var(epsilon_i)=sigma^2. Which of the following statements is not true?

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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Question from the DSE 2012 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.