possum {ipsRdbs}

Body weight and length of possums (tree living furry animals who are mostly nocturnal (marsupial) caught in 7 different regions of Australia.

Description

Body weight and length of possums (tree living furry animals who are mostly nocturnal (marsupial) caught in 7 different regions of Australia.

Usage

possum

Format

A data frame with 101 rows and 3 columns:

Body_Weight

Body weight in kilogram

Length

Body length of the possum

Location

7 different regions of Australia: (1) Western Austrailia (W.A), (2) South Australia (S.A), (3) Northern Territory (N.T), (4) Queensland (QuL), (5) New South Wales (NSW), (6) Victoria (Vic) and (7) Tasmania (Tas).

Source

Lindenmayer and Donnelly (1995).

References

Lindenmayer DBVKLCRB, Donnelly CF (1995). “Morphological variation among columns of the mountain brushtail possum, Trichosurus caninus Ogilby (Phalangeridae: Marsupiala).” Australian Journal of Zoology, 43, 449-458.

Examples

head(possum)
 dim(possum)
 summary(possum)
 ## Code lines used in the book
 ## Create a new data set   
 poss <- possum 
 poss$region <- factor(poss$Location)
 levels(poss$region) <- c("W.A", "S.A", "N.T", "QuL", "NSW", "Vic", "Tas")
 colnames(poss)<-c("y","z","Location", "x")
 head(poss)
 # Draw side by side boxplots 
 boxplot(y~x, data=poss, col=2:8, xlab="region", ylab="Weight")
 # Obtain scatter plot 
 # Start with a skeleton plot 
 plot(poss$z, poss$y, type="n", xlab="Length", ylab="Weight")
 # Add points for the seven regions
 for (i in 1:7) {
    points(poss$z[poss$Location==i],poss$y[poss$Location==i],type="p", pch=as.character(i), col=i)
    }
## Add legends 
 legend(x=76, y=4.2, legend=paste(as.character(1:7), levels(poss$x)),  lty=1:7, col=1:7)
 # Start  modelling 
 #Fit the model with interaction. 
 poss.lm1<-lm(y~z+x+z:x,data=poss)
 summary(poss.lm1)
 plot(poss$z, poss$y,type="n", xlab="Length", ylab="Weight")
 for (i in 1:7) {
 lines(poss$z[poss$Location==i],poss.lm1$fit[poss$Location==i],type="l",
 lty=i, col=i, lwd=1.8)
 points(poss$z[poss$Location==i],poss$y[poss$Location==i],type="p",
 pch=as.character(i), col=i)
 }
 poss.lm0 <- lm(y~z,data=poss)
 abline(poss.lm0, lwd=3, col=9)
 # Has drawn the seven parallel regression lines
 legend(x=76, y=4.2, legend=paste(as.character(1:7), levels(poss$x)), 
 lty=1:7, col=1:7)
 
 n <- length(possum$Body_Weight)
 # Wrong model since Location is not a numeric covariate 
 wrong.lm <- lm(Body_Weight~Location, data=possum)
 summary(wrong.lm)
 
 nis <- table(possum$Location)
 meanwts <- tapply(possum$Body_Weight, possum$Location, mean)
 varwts <- tapply(possum$Body_Weight, possum$Location, var)
 datasums <- data.frame(nis=nis, mean=meanwts, var=varwts)
 datasums <- data.frame(nis=nis, mean=meanwts, var=varwts)
 modelss <- sum(datasums[,2] * (meanwts - mean(meanwts))^2)
 residss <- sum( (datasums[,2] - 1) * varwts)
 
 fvalue <- (modelss/6) / (residss/94)
 fcritical <- qf(0.95, df1= 6, df2=94)
 x <- seq(from=0, to=12, length=200)
 y <- df(x, df1=6, df2=94)
 plot(x, y, type="l", xlab="", ylab="Density of F(6, 94)", col=4)
 abline(v=fcritical, lty=3, col=3)
 abline(v=fvalue, lty=2, col=2)
 pvalue <- 1-pf(fvalue, df1=6, df2=94)
 
 ### Doing the above in R
 # Convert  the Location column to a factor
 possum$Location <- as.factor(possum$Location)
 summary(possum)  # Now Location is a factor 
  
 # Put the identifiability constraint:
 options(contrasts=c("contr.treatment", "contr.poly"))
 colnames(possum) <- c("y", "z", "x")
 # Fit model M1
 possum.lm1 <- lm(y~x, data=possum)
 summary(possum.lm1)
 anova(possum.lm1)
 possum.lm2 <- lm(y~z, data=poss)
 summary(possum.lm2)
 anova(possum.lm2)
 # Include both location and length but no interaction 
 possum.lm3 <-  lm(y~x+z, data=poss)
 summary(possum.lm3)
 anova(possum.lm3)
 # Include interaction effect 
 possum.lm4 <-  lm(y~x+z+x:z, data=poss)
 summary(possum.lm4)
 anova(possum.lm4)
 anova(possum.lm2, possum.lm3)
 #Check the diagnostics for M3
 plot(possum.lm3$fit, possum.lm3$res,xlab="Fitted values",ylab="Residuals", 
 main="Anscombe plot")
 abline(h=0)
 qqnorm(possum.lm3$res,main="Normal probability plot", col=2)
 qqline(possum.lm3$res, col="blue")