case0702 {Sleuth3}

Meat Processing and pH

Description

A certain kind of meat processing may begin once the pH in postmortem muscle of a steer carcass has decreased sufficiently. To estimate the timepoint at which pH has dropped sufficiently, 10 steer carcasses were assigned to be measured for pH at one of five times after slaughter.

Usage

case0702

Format

A data frame with 10 observations on the following 2 variables.

Time

time after slaughter (hours)

pH

pH level in postmortem muscle

Source

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

References

Schwenke, J.R. and Milliken, G.A. (1991). On the Calibration Problem Extended to Nonlinear Models, Biometrics 47(2): 563–574.

See Also

ex0816

Examples

str(case0702)
attach(case0702)

# EXPLORATION
plot(pH ~ Time)  
myLm <- lm(pH ~ Time) 
abline(myLm, col="blue", lwd=2)   
lines(lowess(Time,pH), col="red", lty=2, lwd=2) # Add scatterplot smoother
plot(myLm, which=1)  # Residual plot

logTime <- log(Time)  
plot(pH ~ logTime)  
myLm2   <- lm(pH ~ logTime)  
abline(myLm2)  
plot(myLm2, which=1)  

## PREDICTION BAND ABOUT REGRESSION LINE
xToPredict    <- seq(1,8,length=100) # sequence from 1 to 8 of length 100 
logXToPredict <- log(xToPredict)  
newData       <- data.frame(logTime = logXToPredict)  
myPredict     <- predict(myLm2,newData,    
  interval="prediction", level=.90)  
plot(pH ~ logTime)   
abline(myLm2)  
lines(myPredict[,3]~ logXToPredict, lty=2)  
lines(myPredict[,2] ~ logXToPredict, lty=2) 
# Find smallest time at which the upper endpoint of a 90% prediction 
# interval is less than or equal to 6:
minTime <- min(xToPredict[myPredict[,3] <= 6.0])  
minTime    
abline(v=log(minTime),col="red")   

# DISPLAY FOR PRESENTATION 
plot(pH ~ Time, xlab="Time After Slaughter (Hours); log scale", 
  ylab="pH in Muscle", main="pH and Time after Slaughter for 10 Steers",  
  log="x", pch=21, lwd=2, bg="green", cex=2 ) 
lines(xToPredict,myPredict[,1], col="blue",  lwd=2)  
lines(xToPredict, myPredict[,3], lty=2, col="blue", lwd=2)  
lines(xToPredict, myPredict[,2], lty=2,   col="blue", lwd=2) 
legend(3,7, c("Estimated Regression Line","90% Prediction Band"),   
  lty=c(1,2), col="blue", lwd=c(2,2))  
abline(h=6, lty=3, col="purple", lwd=2)  
text(1.5,6.05,"Desired pH", col="purple")  
lines(c(minTime,minTime),c(5,6.15), col="purple", lwd=2)  
text(minTime,6.2,"4.9 hours",col="purple",cex=1.25)  
  
detach(case0702)