case0902: Why Do Some Mammals Have Large Brains for Their Size?

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

Description

The data are the average values of brain weight, body weight, gestation lengths (length of pregnancy) and litter size for 96 species of mammals.

Usage

case0902

Format

A data frame with 96 observations on the following 5 variables.

Species

species

Brain

average brain weight (in grams)

Body

average body weight (in kilograms)

Gestation

gestation period (in days)

Litter

average litter size

Source

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

See Also

ex0333

Examples

str(case0902)
attach(case0902)

## EXPLORATION                                                                   
myMatrix      <- cbind(Brain, Body, Litter, Gestation)  
if(require(car)){   # Use the car library
scatterplotMatrix(myMatrix,   # Matrix of scatterplots
  smooth=FALSE,    # Omit scatterplot smoother on plots
  diagonal="histogram") # Draw histograms on diagonals
  } 
myLm <- lm(Brain ~ Body + Litter + Gestation)
plot(myLm, which=1)  
logBrain <- log(Brain)
logBody <- log(Body)
logGestation  <- log(Gestation)
myMatrix2 <- cbind(logBrain,logBody,Litter, logGestation) 
if(require(car)){   # Use the car library
  scatterplotMatrix(myMatrix2, smooth=FALSE, diagonal="histogram")  
}
myLm2 <- lm(logBrain ~ logBody + Litter + logGestation)
plot(myLm2,which=1)  # Residual plot.

if(require(car)){   # Use the car library
crPlots(myLm2)  # Partial residual plots (Sleuth Ch.11) 
}
plot(logBrain ~ logBody)
identify(logBrain ~ logBody,labels=Species)   # Identify points on  scatterplot  
# Place the cursor over a point of interest, then left-click.
# Continue with other points if desired. When finished, pres Esc. 

## INFERENCE
summary(myLm2)           
confint(myLm2)           

# DISPLAYS FOR PRESENTATION 
myLm3 <- lm(logBrain ~ logBody + logGestation)
beta <- myLm3$coef
logBrainAdjusted  <- logBrain - beta[2]*logBody  
y <- exp(logBrainAdjusted) 
ymod <- 100*y/median(y) 
plot(ymod ~ Gestation, log="xy",  
  xlab="Average Gestation Length (Days); Log Scale",
  ylab="Brain Weight Adjusted for Body Weight, as a Percentage of the Median", 
  main="Brain Weight Adjusted for Body Weight, Versus Gestation Length, for 96 Mammal Species",
  pch=21,bg="green",cex=1.3)
identify(ymod ~ Gestation,labels=Species, cex=.7) # Identify points, as desired
# Press Esc to complete identify.
abline(h=100,lty=2) # Draw horizontal line at 100%
  
myLm4 <- lm(logBrain ~ logBody + Litter)
beta  <- myLm4$coef
logBrainAdjusted <- logBrain - beta[2]*logBody  
y2 <- exp(logBrainAdjusted)
y2mod <- 100*y2/median(y2)
plot(y2mod ~ Litter, log="y", xlab="Average Litter Size",
  ylab="Brain Weight Adjusted for Body Weight, as a Percentage of the Median",
  main="Brain Weight Adjusted for Body Weight, Versus Litter Size, for 96 Mammal Species",
  pch=21,bg="green",cex=1.3)
identify(y2mod ~ Litter,labels=Species, cex=.7)  
abline(h=100,lty=2)

detach(case0902)

Example output

'data.frame':	96 obs. of  5 variables:
 $ Species  : Factor w/ 96 levels "Aardvark","Acouchis",..: 1 2 3 4 5 6 7 8 9 10 ...
 $ Brain    : num  9.6 9.9 4480 20.3 219 53 210 124 28.5 500 ...
 $ Body     : num  2.2 0.78 2800 2.8 89 6 66 16 3.2 250 ...
 $ Gestation: int  31 98 655 104 218 60 158 183 65 240 ...
 $ Litter   : num  5 1.2 1 1.3 1 2.2 1.2 1.1 4 1.8 ...
Loading required package: car
integer(0)

Call:
lm(formula = logBrain ~ logBody + Litter + logGestation)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.93895 -0.27922 -0.00929  0.28646  1.59743 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept)   0.82338    0.66206   1.244  0.21678    
logBody       0.57455    0.03264  17.601  < 2e-16 ***
Litter       -0.11038    0.04227  -2.611  0.01053 *  
logGestation  0.43964    0.13698   3.210  0.00183 ** 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.4756 on 92 degrees of freedom
Multiple R-squared:  0.9535,	Adjusted R-squared:  0.952 
F-statistic: 629.4 on 3 and 92 DF,  p-value: < 2.2e-16

                  2.5 %      97.5 %
(Intercept)  -0.4915254  2.13829063
logBody       0.5097143  0.63937813
Litter       -0.1943220 -0.02643223
logGestation  0.1675856  0.71169994
integer(0)
integer(0)

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