1. What are the two conflicting objectives of regression model building using on
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Question
1. What are the two conflicting objectives of regression model building using only a subset of the regressors?
2. Suppose we have K candidate regressors in the full model. Let a subset model with p regressors was fitted by deleting r regressors sothat p-1 =K-r.
(a) Briefly describe the properties of the estimates obtained from the subset model.
3. Summarize the consequences of model misspecification due to deletion of variables. What are the criteria for evaluating and comparing subset regression model?
4. Describe Forward selection, Backward elimination and Stepwise regression models for selecting a best fitted final model.
5. What are the basic steps to be followed in our strategy for variable selection and model building?
Explanation / Answer
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1) Building a regression model that includes only a subset of the available regressors involves two conflicting objectives:
(a) We would like the model to include as many regressors as possible so that information content in these factors can influence the predicted value of y .
(b) We want the model to include as few regressors as possible because the variance of the prediction y ) increases as the number of regressors increases.
By deleting variables from the model, we may improve the precision of the parameter estimates of the retained variables even though some of the deleted variables are not negligible. This is also true for the variance of a predicted response.
Deleting variables potentially introduces bias into the estimates of the coefficient of retained variables and the response. Over-fitting a model (including variables in the model with truly zero regression coefficients in the population) will not introduce bias when population regression coefficient estimated, if the usual regression assumptions are met. We must, however, to ensure that over-fitting does not introduce harmful collinearity.
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