Suppose from the estimation of a linear regression model the residual sum of squares and the total sum of squares are obtained as 44 and 80, respectively. The value of coefficient of determination is ______ (round off to two decimal places).
GATE 2023 Question 63: Goodness of fit and model selection
Answer and worked solution
Answer: 0.43 to 0.47
The coefficient of determination is defined as:
Therefore 0.45, within the key's accepted range of 0.43 to 0.47.
The trap: 0.55
A common slip is computing and stopping there, forgetting the final step required to get itself, rather than the unexplained fraction of variance.
Plain-text version
Suppose from the estimation of a linear regression model Yᵢ = β₀+β₁Xᵢ+eᵢ the residual sum of squares and the total sum of squares are obtained as 44 and 80, respectively. The value of coefficient of determination is (round off to two decimal places).
Also written as: Suppose from the estimation of a linear regression model Y_i = beta_0+beta_1X_i+e_i the residual sum of squares and the total sum of squares are obtained as 44 and 80, respectively. The value of coefficient of determination is (round off to two decimal places).
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 GATE 2023 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.