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Questions › DSE › DSE 2019 › Q37
0 marksEconometrics › Goodness of fit and model selection › Adjusted R-squared and model comparisonModerateabout 2 min

DSE 2019 Question 37: Goodness of fit and model selection

Scenario 3: Data from a random sample of 107 home sales in 2003 yielded the regression P^=119.2+0.485 BD+23.4 BA+0.156 HS+0.002 PS+0.090 A−35.6 PC\hat P=119.2+0.485\,BD+23.4\,BA+0.156\,HS+0.002\,PS+0.090\,A-35.6\,PCP^=119.2+0.485BD+23.4BA+0.156HS+0.002PS+0.090A−35.6PC, with standard errors (23.9),(2.61),(10.76),(0.011),(0.00048),(0.311),(10.5)(23.9),(2.61),(10.76),(0.011),(0.00048),(0.311),(10.5)(23.9),(2.61),(10.76),(0.011),(0.00048),(0.311),(10.5) respectively. R2=0.72R^2=0.72R2=0.72, SER=41.5SER=41.5SER=41.5. PPP is price or value (Rs. 1000), BDBDBD is number of bedrooms, BABABA is number of baths, HSHSHS is house size (sq. ft.), PSPSPS is plot size (sq. ft.), AAA is age (years), and PCPCPC is a dummy =1=1=1 if the house is in poor condition and 000 otherwise.

What is the adjusted coefficient of determination?

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Scenario 3: Data from a random sample of 107 home sales in 2003 yielded the regression P̂=119.2+0.485 BD+23.4 BA+0.156 HS+0.002 PS+0.090 A-35.6 PC, with standard errors (23.9),(2.61),(10.76),(0.011),(0.00048),(0.311),(10.5) respectively. R²=0.72, SER=41.5. P is price or value (Rs. 1000), BD is number of bedrooms, BA is number of baths, HS is house size (sq. ft.), PS is plot size (sq. ft.), A is age (years), and PC is a dummy =1 if the house is in poor condition and 0 otherwise. What is the adjusted coefficient of determination? (A) 0.7052 (B) 0.7022 (C) 0.7032 (D) 0.7042

Also written as: Scenario 3: Data from a random sample of 107 home sales in 2003 yielded the regression P_hat=119.2+0.485 BD+23.4 BA+0.156 HS+0.002 PS+0.090 A-35.6 PC, with standard errors (23.9),(2.61),(10.76),(0.011),(0.00048),(0.311),(10.5) respectively. R^2=0.72, SER=41.5. P is price or value (Rs. 1000), BD is number of bedrooms, BA is number of baths, HS is house size (sq. ft.), PS is plot size (sq. ft.), A is age (years), and PC is a dummy =1 if the house is in poor condition and 0 otherwise. What is the adjusted coefficient of determination?

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

What this question tests

This question is on Adjusted R-squared and model comparison, part of Goodness of fit and model selection in Econometrics.

Penalising extra regressors and when R-squared can be compared across models.

TestStop has 7 past-paper questions on this subtopic; the nearest in year are below.

  • IIT JAM 2022 · Q27Which of the following is NOT correct regarding R-squared (R²) and adjusted R-squared (R̄²)?
Practise Goodness of fit and model selectionMore on Adjusted R-squared and model comparison

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Question from the DSE 2019 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.