# 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

1 |

### 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

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)
``` |

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