Variable selection methods a. The following questions is a variable selection me
ID: 3232020 • Letter: V
Question
Variable selection methods a. The following questions is a variable selection method based on AIC. Is this forward selection or backward elimination method? Explain. II. If no variable is added or removed from the original model, what will happen to the AIC of the original mode? III. Which one of the variables will drop AIC the most when added to the original model (mpg-1). IV. Write the value of the AIC of the model when this variable (from part III) is added to the model. V. Which one of the variables can you say for sure will be in the final model. b. Explain briefly how the F-statistic is used when adding variables to model that begins with no predictors. What the difference between forward selection and stepwise regression?Explanation / Answer
1) This is a forward selection procedure. As we can see that the initial model is without any predictors.
2) If no variable is added to the original model, the AIC of the original model is 115.94. This is just a null model with only intercept term and no predictors. This model will just predict the average value of mpg.
3) weight variable will drop the AIC value the most when added to the original model.
4) On addition of weight variable, the AIC value of the model will drop from 115.94 to 73.217.
5) weight variable seems to be the most important predictor among the given variables as it decreases the AIC value the most.
b) F statistic is used to test whether the model is better than the null model which only produces average. If the p value associated with the F statistic is significant, we can reject the null hypothesis.
c) In stepwise regression, you combine the forward and backward stepwise approaches. Variables are entered one at a time but at each step, the variables in the model are reevaluated and those that dont contribute to the model are deleted. In forward selection, you add predictor variables to the model one at a time, stopping when addition of variables would no longer improve the model.
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