# case0702: Meat Processing and pH In Sleuth3: Data Sets from Ramsey and Schafer's "Statistical Sleuth (3rd Ed)"

## 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

 `1` ```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.

`ex0816`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47``` ```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) ```