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408    CHAPTER 16. VARIABLE SELECTION AND MODEL BUILDING


                                 extractAIC(hipcenter_mod_best_bic, k = log(n))


                                 ## [1]    2.0000 278.3418


                                 extractAIC(hipcenter_mod_back_bic, k = log(n))


                                 ## [1]    2.0000 278.7306

                                 extractAIC(hipcenter_mod_forw_bic, k = log(n))


                                 ## [1]    2.0000 278.3418

                                 extractAIC(hipcenter_mod_both_bic, k = log(n))


                                 ## [1]    2.0000 278.3418



                                 16.3     Higher Order Terms


                                 So far we have only allowed first-order terms in our models. Let’s return to the
                                 autompg dataset to explore higher-order terms.

                                 autompg = read.table(
                                   "http://archive.ics.uci.edu/ml/machine-learning-databases/auto-mpg/auto-mpg.data",
                                   quote = "\"",
                                   comment.char = "",
                                   stringsAsFactors = FALSE)
                                 colnames(autompg) = c("mpg", "cyl", "disp", "hp", "wt", "acc",
                                                        "year", "origin", "name")
                                 autompg = subset(autompg, autompg$hp != "?")
                                 autompg = subset(autompg, autompg$name != "plymouth reliant")
                                 rownames(autompg) = paste(autompg$cyl, "cylinder", autompg$year, autompg$name)
                                 autompg$hp = as.numeric(autompg$hp)
                                 autompg$domestic = as.numeric(autompg$origin == 1)
                                 autompg = autompg[autompg$cyl != 5,]
                                 autompg = autompg[autompg$cyl != 3,]
                                 autompg$cyl = as.factor(autompg$cyl)
                                 autompg$domestic = as.factor(autompg$domestic)
                                 autompg = subset(autompg, select = c("mpg", "cyl", "disp", "hp",
                                                                        "wt", "acc", "year", "domestic"))
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