# Body weight and length of possums (tree living furry animals who are mostly nocturnal (marsupial) caught in 7 different regions of Australia. ## 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 if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_citeOnly(keys="Lindenmayer1995;textual",package="ipsRdbs",cached_env=.Rdpack.currefs) . ```r possum ``` ## Examples ```r 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") ``` ## References if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_all_ref(.Rdpack.currefs)

possum dataset