# 10_11 - STAT 420 Examples for Fall 2007 1 The worksheet case1201.csv contains data on the average SAT scores by state The states have been ordered

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STAT 420 Examples for 10/11/2007 Fall 2007 1. The worksheet case1201.csv contains data on the average SAT scores by state. The states have been ordered by how well their students did on the SAT on average. Researchers have tried to explain the state by state differences in scores. Column 2 is the average SAT scores, along with six variables that may be associated with the SAT differences among states: percentage of the total eligible students who took the exam, median income of families of test takers, average number of years that the test takers had formal studies in social studies, natural sciences, humanities, percentage of test takers who attended public secondary schools, total state expenditure on secondary schools (dollars per student), and median percentile ranking of the test takers within their secondary school classes. > case1201.dat <- read.table("http://www.stat.uiuc.edu/~stepanov/case1201.csv", header=T, sep=",") > pairs(SAT ~ TAKERS+INCOME+YEARS+PUBLIC+EXPEND+RANK, case1201.dat)

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> pairs(SAT ~ log(TAKERS)+INCOME+YEARS+PUBLIC+EXPEND+RANK, case1201.dat) > case1201.dat <- subset(case1201.dat, STATE != "Alaska") > case1201.fit <- lm(SAT ~ log(TAKERS)+INCOME+YEARS+PUBLIC+EXPEND+RANK, case1201.dat) A KAIKE S I NFORMATION C RITERION (AIC): Akaike proposed to choose the model that minimises AIC = – 2 × (Maximized log-likelihood) + 2 × (number of parameters in the model) = n + n ln ( 2 π ) + n ln ( RSS / n ) + 2 p R: AIC = n ln ( RSS / n ) + 2 p
B ACKWARD E LIMINATION > step(case1201.fit, direction = "backward") Start: AIC= 311.88 SAT ~ log(TAKERS) + INCOME + YEARS + PUBLIC + EXPEND + RANK Df Sum of Sq RSS AIC - PUBLIC 1 20 21417 310 - INCOME 1 340 21737 311 <none> 21397 312 - log(TAKERS) 1 2150 23547 315 - YEARS 1 2532 23928 315 - RANK 1 2679 24076 316 - EXPEND 1 10964 32361 330 Step: AIC= 309.93 SAT ~ log(TAKERS) + INCOME + YEARS + EXPEND + RANK Df Sum of Sq RSS AIC - INCOME 1 505 21922 309 <none> 21417 310 - log(TAKERS) 1 2552 23968 313 - YEARS 1 3011 24428 314

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## This note was uploaded on 04/29/2010 for the course STAT stat 420 taught by Professor Stepanov during the Spring '07 term at University of Illinois at Urbana–Champaign.

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10_11 - STAT 420 Examples for Fall 2007 1 The worksheet case1201.csv contains data on the average SAT scores by state The states have been ordered

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