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Using the RateMy Professor (Rateprof) dataset from alr4, we will explore the process of the stepwise method quality is the reb) How many possible models are within the scope we have defined above (no interactions, between the simplest model and the mi) How many models did R fit in this backward elimination process? (ii) Give an example of a model that has more than 4 predi

Using the RateMy Professor (Rateprof) dataset from alr4, we will explore the process of the stepwise method quality is the response variable. gender, numYears, numRaters, numCourses, pepper, discipline, dept, helpfulness, clarity, easiness, raterInterest are the predictor variables. For simplicity, interactions are not considered. To understand the meaning of the variables, please use the code ?Rateprof after you import the library alr4. Consider quality ~1 to be the simplest model under consideration, and quality~ 1 + gender+ numYears+numRaters+ numCourse s + pepper+ dept +helpfulness + clarity - easiness + raterinterest is the most complicated model under consideration. (a) Which of the following model will have the highest R2? Please explain your decision. (A) quality ~1 (B) quality ~1 + gender numYears + numRaters numCoursespepper dept + helpfulness + clarity + easiness + raterInterest (C) quality ~1 + gender + numYears + numRaters + numCourses (D) quality ~1 + dept + helpfulness + clarity easiness
b) How many possible models are within the scope we have defined above (no interactions, between the simplest model and the most complicated model)? Le., how many subsets total when considering all subsets? Please explain how you obtain the answer. Note: the simplest model and the most complicated model should be included in the count (c) Please use the backward elimination method with AIC, starting with the most complicated model. Note: you should provide the code and the R output of the backward elimination method (i) What final model is selected? Please write out the fitted model.
i) How many models did R fit in this backward elimination process? (ii) Give an example of a model that has more than 4 predictors, but has not been fitted in this backward elimination process? Please use the format of Y ~1 +x1 +r2. (d) Please use the backward elimination method with BIC, starting with the most complicated model. Note: you should provide the code and the R output of the backward elimination method. (i) What final model is selected? Please write out the fitted model. Is this model the same as the one selected by the backward elimination process with AIC (Part (c))? ii) Why could AIC and BIC lead to different final models? (e) Use the forward selection method with AIC, starting with the simplest model (the intercept model) with the potential to go to the most complicated model. Note: you should provide the code and the R output of the forward selection method (a) What model is selected? Please write down the fitted model. (b) Is the result consistent with that of Part (c)? Please answer yes or no. (c) Is the final model of backward elimination with AIC always consistent with the final model of forward elimination with AIC? Please explain your decision.
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