3. For question 3, use the following R outputs for the four different models. (n

Question

3. For question 3, use the following R outputs for the four different models. (n = 97) rnO= 1m(Ipsa-1, data=prostate) sum(resid (mo) 2) 1 127.9176 model-1-Im( Ipsa-lcavol+1weight .data= prostate) sum (resid (model1) 2) 1 52.96626 model-2 = 1m( Ipsa" I c a vol+1weight+svi, data-, prostate) sum(resid (model2) 2) 1 47.78486 model-3 = Inn(1psa-lcavol+1weight+svi+1bph.data= prostate) sum(resid (model3) 2) 1 46.4848 model-4-lm(1psa. I c a vol+1weight+svi+1bph+1cp , data-prostate ) sum(resid (model4) 2) 146.38251 (a) Find the best models in terms of AIC and BIC, respectively. (1 pt) (b) Find the best model in terms of adjusted R2. (1 pt) (c) Compare model 1 and 3 using an F-test at = 0.05. Was the difference significant? (1 pt (d) Compare model 2 and 3 using an F-test at = 0.05. Was the difference significant? (1

Explanation / Answer

Summary statistics or AIC, BIC, R2 values are not given. But you can use general concept to select the best model.

(a) Model having the lowest value of AIC and BIC is the best model.

AIC and BIC are measures of goodness of fit. They penalize complex models. In other words, it penalize the higher number of estimated parameters. It believes in a concept that a model with fewer parameters is to be preferred to one with more. Suppose you have two models, the model with the lower AIC and BIC score is better.

(b) Model having high value of adjusted R2 is the best model.

(c) For model 1 and 3, if the p-value for F-test is below alpha=0.05 then that model will be significant.

(d) For model 2 and 3, if the p-value for F-test is below alpha=0.05 then that model will be significant.

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