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Questions › DSE › DSE 2016 › Q7
0 marksEconometrics › Linear regression and OLS › The regression model and the OLS estimatorHardabout 3 min

DSE 2016 Question 7: Linear regression and OLS

The parameters of the following multiple regression model have been estimated using OLS: Y=β1+β2X2+β3X3+ϵY=\beta_{1}+\beta_{2}X_{2}+\beta_{3}X_{3}+\epsilonY=β1​+β2​X2​+β3​X3​+ϵ. Denote the estimated residuals from this regression as eee. Which of the following statements is false?

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The parameters of the following multiple regression model have been estimated using OLS: Y=β₁+β₂X₂+β₃X₃+ϵ. Denote the estimated residuals from this regression as e. Which of the following statements is false? (A) The R-squared from the regression of e on a constant, X₂ and X₃ is zero (B) The R-squared from the regression of Y on a constant and Ŷ is the same as in the original regression (Ŷ stands for the estimated value of Y) (C) The slope coefficient from the regression of Y on a constant and Ŷ is 1 and the intercept is 0 (D) The R-squared from the regression of Y on a constant and e is the same as in the original regression

Also written as: The parameters of the following multiple regression model have been estimated using OLS: Y=beta_1+beta_2X_2+beta_3X_3+epsilon. Denote the estimated residuals from this regression as e. Which of the following statements is false?

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 2016 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.