Skip to content
We use only essential cookies to keep you signed in and remember your preferences. See our Cookie Policy.
TestStop
MocksPracticeResourcesIndiaBlogPricing
Sign in
Questions › DSE › DSE 2013 › Q47
2 marksEconometrics › Goodness of fit and model selection › R-squared and the coefficient of determinationModerateabout 2 min

DSE 2013 Question 47: Goodness of fit and model selection

A linear regression model y=α+βx+εy=\alpha+\beta x+\varepsilony=α+βx+ε is estimated using OLS. It turns out that the estimated R2R^2R2 equals zero. This implies that:

Tap an option to check your answer.

Answer and worked solution

Checking your account…

Plain-text version

A linear regression model y=α+β x+ε is estimated using OLS. It turns out that the estimated R² equals zero. This implies that: (A) All x 's are necessarily zero (B) β̂=1 and y=α̂+x (C) β̂=0 or all x 's are constant (D) There are no implications for β̂

Also written as: A linear regression model y=alpha+beta x+epsilon is estimated using OLS. It turns out that the estimated R^2 equals zero. This implies that:

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.

TestStop has 15 past-paper questions on this subtopic; the nearest in year are below.

  • GATE 2023 · Q63Suppose from the estimation of a linear regression model Yᵢ = β₀+β₁Xᵢ+eᵢ the residual sum of squares and the…
Practise Goodness of fit and model selectionMore on R-squared and the coefficient of determination

Similar questions from other papers

  • CUET-PG 2025 · Q62Coefficient of determination measures (A) correlation between the dependent and independent variables. (B) the residual sum of squares as a proportion of the total sum…
  • GATE 2025 · Q49Consider a two-variables (x,y) linear regression model y = α + β x + ε where α and β are the parameters, and ε is the error term. The parameters are estimated using the…
  • IIT JAM 2025 · Q15In the context where sample mean of the dependent variable (Ȳ) lies closer to the observed Yᵢ than its least square predictor (Ŷᵢ),.
  • UGC-NET 2025 · Q74The Coefficient of Determination (R²): A. is an increasing function of the number of regressors B. is a decreasing function of the number of regressors C. is unaffected…
  • IIT JAM 2024 · Q53A regression equation Y = -2.5 + 2X is estimated using Y = 2, 5, 9, 14 and X = 2, 4, 6, 8. The coefficient of determination is (rounded off to two decimal places).

Question from the DSE 2013 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.