(20pt) We have 4 independent variables X1, X2, X3 and X4. The table as below pro
ID: 3312135 • Letter: #
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(20pt) We have 4 independent variables X1, X2, X3 and X4. The table as below provides R2 adjusted R2 and BIC of 15 different OLS models. Column "Independent variables" includes the set of independent variables contained in each OLS regression Independent variablesR Adj R BIC 0.00110.0010 823.049 0.16160.1574 788.009 0.52740.5250673.3828 0.00470.0040822.3285 0.16180.1533793.2606 0.53420.5294 675.7815 0.0059 0.0050827.3785 0.67660.6733 602.8175 0.16750.1590 791.9065 0.54260.5379 672.1306 0.68060.6757 605.5908 0.16770.1550 797.1405 0.55020.5433 674.084 0.69360.6889597.2843 0.69830.6921599.4996 2 3 X1,X2 X3,X4 X1,X2,X3 X1,X3,X4 X1,X2,X3,X4 (b) Use forward stepwise selection and BIC criterion to choose the best model. Please carefully explain your procedure.Explanation / Answer
Using forward selection,
1. The first varibale selected will be X3 as BIC is lowest for X3 among the models X1, X2, X3 and X4.
2. Then after X3, X2 will get selected because the model (X2,X3) has the lowest BIC among the models (X1,X3), (X2,X3) and (X3,X4)
3. Then after X3,X2 ; X4 will get selected because the model (X2,X3,X4) has the lowest BIC among the models (X1,X2,X3), (X2,X3,X4).
4. After that X1 will not get selected as the BIC of(X1,X2,X3,X4) is less than the BIC of (X2,X3,X4)
Hence, using forward selection and BIC criterion, the model (X2,X3,X4) will get selected.
The model X2, X3, X4 has the lowest BIC value among all these models
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