3. (20pt) We have 4 independent variables X1, X2.3 and X4. The table as below pr

Question

3. (20pt) We have 4 independent variables X1, X2.3 and X4. The table as below provides R2 adjusted R and BIC of 15 different OLS models. Column Independent variables" ncludes the set of independent variables contained in each OLS regression. Independent variables RAdj RBIC 0.00110.0010 823.049 0.1616 0.1574 788.009 0.52740.5250 673.3828 0.0047 0.0040 822.3285 0.1618 0.1533 793.2606 0.5342 0.5294 675.7815 0.0059 0.0050 827.3785 0.6766 0.6733 602.8175 0.16750.1590 791.9065 0.5426 0.5379 672.1306 0.6806 0.6757 605.5908 0.1677 0.1550797.1405 0.5502 0.5433 674.084 0.6936 0.6889 597.2843 0.6983 0.6921 599.4996 X1,X2 X2,X3 X1,X2,X3 X1, X2,X4 X1,X3,X4 X1,X2,X3,X4

Explanation / Answer

Backward stepwise selection procedure based on BIC criteria.

The BIC of the full model X1, X2, X3 and X4 is 605.59.

The best model based on the minimum BIC for three independent variables is X1, X2 and X3 with corresponding BIC 605.59. Compare the above two model BIC, for increasing an independent variable decrease 5 DIC at full model. This 5 is not good enough to increase a variable. Hence, the model of variables X1, X2 and X3 is better than full model.

The best model for two independent variables is X2, X3 with the corresponding BIC=602.82. Similar to the above expression, the model of variable X2 and X3 is better than the model of variables X1, X2 and X3.

Again, the best model for one independent variable is X3 with the corresponding BIC=673.38. Here, for increased a variable in the model of variable X2, X3 decreases 70.56 in BIC. Hence, the best model for the given variables combination is the model of the independent variable X2 and X3.

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