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

Question

3. (20pt) We have 4 independent variables X1, X2, Xs and X4. The table as below provides R2 adjusted R2 and BIC of 15 different OLS models. ColumnIndependent variables" includes the set of independent variables contained in each OLS regression R21 Adj-R2 0.0011 0.0010 823.049 0.16160.1574 788.009 0.52740.5250 673.3828 0.0047 0.0040 822.3285 0.16180.1533 793.2606 0.5342 0.5294 675.7815 0.00590.0050 827.3785 0.67660.6733 602.8175 0.1675 0.1590 791.9065 0.54260.5379 672.1306 0.68060.6757 605.5908 0.16770.1550 797.1405 0.5502 0.5433 674.084 0.6936 0.6889597.2843 0.69830.6921 599.4996 Independent variables R BIC X2,X3,X4 (a) Use best subset selection and BIC criterion to choose the best model. Please carefully explain your procedure.

Explanation / Answer

For checking model adequacy, using given three Critaterian, We intepreate as Lower the BIC better the model and higher the R2 and AdjR2 better the model.

Using this criterian we can esily see that variable X1 and X4 does not have sufficient role in model builinding.

but if its medical related or any other data in which we cant drop the variavble then we have to include that variable and make model. and we have too select higher interaction effect criterian. in includuing higher interaction effect lower interaction effect are already included.

Here, not specified about the data. Hence we drop that variable and make model.

poissible model is,

(1)using only droping X1 since its have lower R2 and higher BIC. and include all other variable's main as well as interaction model.then,

Y=X2+X3+X4+X2.X3+X3.X4+X2.X4+X2.X3.X4

then R2=0.6936 AdjR2=0.6889 and BIC=597.2843

(2)

using only droping X4 since its have lower R2 and higher BIC. and include all other variable's main as well as interaction model.then,

Y=X2+X3+X1+X2.X3+X3.X1+X2.X1+X2.X3.X1

then R2=0.6806 AdjR2=0.6757 and BIC=605.5908

(3)

using only droping X1 and X4 both. since its have lower R2 and higher BIC. and include all other variable's main as well as interaction model.then,

Y=X2+X3+X2.X3

then R2=0.6766 AdjR2=0.6733 and BIC=602.8175

In camparision of this three model if we have to select a model based on criterian then we go with 1st model as its have lower BIC then other and if want to select the model based on coplexicity then we go with model 3 as less the variable include less the comlicated.

since, all the three model have model choosing criterian approximately near the saturated model. we can used any one of three.as there is no science for model chooing its art which developed using expirence.

Related Questions

Navigate

• Browse (All)
• Browse 3
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.