possum: Body weight and length of possums (tree living furry animals...

In ipsRdbs: Introduction to Probability, Statistics and R for Data-Based Sciences

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

\insertCite

Lindenmayer1995;textualipsRdbs.

References

\insertAllCited

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")
 

ipsRdbs documentation built on May 29, 2024, 4:15 a.m.