case0801: Island Area and Number of Species

In Sleuth3: Data Sets from Ramsey and Schafer's "Statistical Sleuth (3rd Ed)"

Description

The data are the numbers of reptile and amphibian species and the island areas for seven islands in the West Indies.

Usage

case0801

Format

A data frame with 7 observations on the following 2 variables.

Area

area of island (in square miles)

Species

number of reptile and amphibian species on island

Source

Ramsey, F.L. and Schafer, D.W. (2013). The Statistical Sleuth: A Course in Methods of Data Analysis (3rd ed), Cengage Learning.

References

Wilson, E.O., 1992, The Diversity of Life, W. W. Norton, N.Y.

Examples

str(case0801)
attach(case0801)

## EXPLORATION
logSpecies <- log(Species)   
logArea  <- log(Area) 
plot(logSpecies ~ logArea, xlab="Log of Island Area",
  ylab="Log of Number of Species",
  main="Number of Reptile and Amphibian Species on 7 Islands")
myLm <- lm(logSpecies ~ logArea)    
abline(myLm)  

## INFERENCE AND INTERPRETATION
summary(myLm) 
slope     <- myLm$coef[2]   
slopeConf <- confint(myLm,2) 
100*(2^(slope)-1)   # Back-transform estimated slope
100*(2^(slopeConf)-1) # Back-transform confidence interval 
# Interpretation: Associated with each doubling of island area is a 19% increase 
# in the median number of bird species (95% CI: 16% to 21% increase).

## DISPLAY FOR PRESENTATION
plot(Species ~ Area, xlab="Island Area (Square Miles); Log Scale",  
  ylab="Number of Species; Log Scale", 
  main="Number of Reptile and Amphibian Species on 7 Islands",
  log="xy", pch=21, lwd=2, bg="green",cex=2 )    
dummyArea <- c(min(Area),max(Area)) 
beta <- myLm$coef  
meanLogSpecies <-  beta[1] + beta[2]*log(dummyArea)   
medianSpecies  <-  exp(meanLogSpecies)  
lines(medianSpecies ~ dummyArea,lwd=2,col="blue") 
island <- c(" Cuba"," Hispaniola"," Jamaica", " Puerto Rico", 
  " Montserrat"," Saba"," Redonda")  
for (i in 1:7) {   
   offset <- ifelse(Area[i] < 10000, -.2, 1.5)  
   text(Area[i],Species[i],island[i],col="dark green",adj=offset,cex=.75) }  
    
detach(case0801)

Example output

'data.frame':	7 obs. of  2 variables:
 $ Area   : int  44218 29371 4244 3435 32 5 1
 $ Species: int  100 108 45 53 16 11 7

Call:
lm(formula = logSpecies ~ logArea)

Residuals:
         1          2          3          4          5          6          7 
-0.0021358  0.1769753 -0.2154872  0.0009468 -0.0292440  0.0595428  0.0094020 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  1.93651    0.08813   21.97 3.62e-06 ***
logArea      0.24968    0.01211   20.62 4.96e-06 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.1283 on 5 degrees of freedom
Multiple R-squared:  0.9884,	Adjusted R-squared:  0.9861 
F-statistic: 425.3 on 1 and 5 DF,  p-value: 4.962e-06

 logArea 
18.89433 
         2.5 %   97.5 %
logArea 16.357 21.48699

Sleuth3 documentation built on May 2, 2019, 6:41 a.m.