case1201 {Sleuth3}

State Average SAT Scores

Description

Data on the average SAT scores for US states in 1982 and possible associated factors.

Usage

case1201

Format

A data frame with 50 observations on the following 8 variables.

State

US state

SAT

state averages of the total SAT (verbal + quantitative) scores

Takers

the percentage of the total eligible students (high school seniors) in the state who took the exam

Income

the median income of families of test–takers (in hundreds of dollars)

Years

the average number of years that the test–takers had formal studies in social sciences, natural sciences and humanities

Public

the percentage of the test–takers who attended public secondary schools

Expend

the total state expenditure on secondary schools (in hundreds of dollars per student)

Rank

the median percentile ranking of the test–takers within their secondary school classes

Source

Ramsey, F.L. and Schafer, D.W. (2013). The Statistical Sleuth: A Course in Methods of Data Analysis (3rd ed), Cengage Learning.

Examples

str(case1201)
attach(case1201)

## EXPLORATION
logTakers  <- log(Takers)
myMatrix   <- cbind(SAT, logTakers,Income, Years, Public, Expend, Rank)
if(require(car)){   # Use the car library   
scatterplotMatrix(myMatrix, diagonal="histogram", smooth=FALSE)  
  }                  
State[Public < 50] # Identify state with low Public (Louisiana)
State[Expend > 40] # Alaska
myLm1    <- lm(SAT ~ logTakers + Income+ Years + Public + Expend + Rank)
plot(myLm1,which=1)         
plot(myLm1,which=4)  # Cook's Distance       
State[29] # Identify State number 29?  ([1] Alaska) 
plot(myLm1,which=5)        
if(require(car)){   # Use the car library   
  crPlots(myLm1)  # Partial residual plot
}
myLm2 <- update(myLm1, ~ . ,subset=(State != "Alaska"))  
plot(myLm2,which=1)
plot(myLm2,which=4)
if(require(car)){   # Use the car library   
  crPlots(myLm2) # Partial residual plot
}
## RANK STATES ON SAT SCORES, ADJUSTED FOR Takers AND Rank
myLm3        <- lm(SAT ~ logTakers + Rank) 
myResiduals  <- myLm3$res 
myOrder      <- order(myResiduals)  
State[myOrder] 

## DISPLAY FOR PRESENTATION
dotchart(myResiduals[myOrder], labels=State[myOrder],
  xlab="SAT Scores, Adjusted for Percent Takers and HS Ranks (Deviation From Average)",
  main="States Ranked by Adjusted SAT Scores",
  bg="green", cex=.8)
abline(v=0, col="gray")

## VARIABLE SELECTION (FOR RANKING STATES AFTER ACCOUNTING FOR ALL VARIABLES)
expendSquared <- Expend^2   
if(require(leaps)){   # Use the leaps library   
  mySubsets   <- regsubsets(SAT ~ logTakers + Income+ Years + Public + Expend + 
    Rank + expendSquared, nvmax=8, data=case1201, subset=(State != "Alaska")) 
  mySummary <- summary(mySubsets) 
  p <- apply(mySummary$which, 1, sum) 
  plot(p, mySummary$bic, ylab = "BIC")  
  cbind(p,mySummary$bic) 
  mySummary$which[4,]  
  myLm4 <- lm(SAT ~ logTakers + Years + Expend + Rank, subset=(State != "Alaska"))
  summary(myLm4)

## DISPLAY FOR PRESENTATION
  myResiduals2 <- myLm4$res
  myOrder2 <- order(myResiduals2)
  newState <- State[State != "Alaska"]
  newState[myOrder2] 
  dotchart(myResiduals2[myOrder2], labels=State[myOrder2],
    xlab="Adjusted SAT Scores (Deviation From Average Adjusted Value)",
    main=paste("States Ranked by SAT Scores Adjusted for Demographics",
               "of Takers and Education Expenditure", sep = " "),
    bg="green", cex = .8)
  abline(v=0, col="gray")
}

detach(case1201)