Sleuth3 (version 0.1-8)

case1201: State Average SAT Scores

Description

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

Usage

case1201

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)