Animal Mass vs. Basal Metabolic Rate

The data file below contains data about the average mass (in grams) and the average basal metabolic rate (BMR) measured in watts for 315 different species of mammals.

mammals = read.csv("http://people.hsc.edu/faculty-staff/blins/StatsExamples/KleibersLaw.csv")
head(mammals)
##                  Species     Class     Mass   BMR
## 1      Acinonyx jubatus  Mammalia  46500.00 61.77
## 2       Acomys russatus  Mammalia     45.00  0.24
## 3    Acrobates pygmaeus  Mammalia     13.00  0.08
## 4 Aepyprymnus rufescens  Mammalia      2.48  5.98
## 5       Ailurus fulgens  Mammalia   4950.00  4.90
## 6     Alouatta palliata  Mammalia   6000.00 11.46
myLM = lm(BMR~Mass,data=mammals)
plot(mammals$Mass,mammals$BMR,ylab='Average BMR (Watts)',xlab="Average Mass (g)")
abline(myLM)

Exercises

  1. Try log-transforming one or both of the x and y-variables. Which tranformation produces the best pictures?

  2. Find the trasformed least squares regression line.

  3. Check the residuals to see if they have roughly constant variance and following a normal distribution.

  4. Make a confidence interval for the BMR of a species with an average body mass of 4,000 grams. What are you 95% sure that your confidence interval contains?

  5. Use pencil and paper to convert the log-transformed linear model to the appropriate nonlinear model, and describe whether it is an exponential, logarithmic, or power law model.

  6. Do your results fit with Kleiber’s law?