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Questions › DSE › DSE 2016 › Q11
0 marksEconometrics › Goodness of fit and model selection › R-squared and the coefficient of determinationModerateabout 2 min

DSE 2016 Question 11: Goodness of fit and model selection

In the OLS regression Yi=β1+β2Xi+uiY_{i}=\beta_{1}+\beta_{2}X_{i}+u_{i}Yi​=β1​+β2​Xi​+ui​, suppose the coefficient of determination is estimated to be 0.60.60.6. We now transform the variables such that Yi∗=0.5YY_{i}^{*}=0.5YYi∗​=0.5Y and Xi∗=0.75XiX_{i}^{*}=0.75X_{i}Xi∗​=0.75Xi​ and re-run the regression. The coefficient of determination is now:

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In the OLS regression Yᵢ=β₁+β₂Xᵢ+uᵢ, suppose the coefficient of determination is estimated to be 0.6. We now transform the variables such that Yᵢ*=0.5Y and Xᵢ*=0.75Xᵢ and re-run the regression. The coefficient of determination is now: (A) 0.6 (B) 0.4 (C) 0.9 (D) 0.3

Also written as: In the OLS regression Y_i=beta_1+beta_2X_i+u_i, suppose the coefficient of determination is estimated to be 0.6. We now transform the variables such that Y_i*=0.5Y and X_i*=0.75X_i and re-run the regression. The coefficient of determination is now:

Goodness of fit and model selection has come up 27 times in 6 exams since 2009.

What this question tests

This question is on R-squared and the coefficient of determination, part of Goodness of fit and model selection in Econometrics.

The share of variation in the dependent variable that the regression explains.

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