6.085 Problem Set Two
Regression

The CSV file contains various biological data from several species of
bats (source: Mating System and brain size in bats, Pitnick et. al.).
The BodyMass, BrainMass, and TestesMass columns are all in grams.  The
NeoCortexVolume is in mm^3.  Female Promiscuity indicates whether
female bats mate with multiple males during their lifetime.  Finally,
diet=1 indicates a fruit-based diet; diet=2 indicates an "other" diet.
Complete the following analysis:

1. Biologists usually use the log units for regression analysis.  What
   is the underlying assumption when using log units instead of
   standard units?  For the rest of the assignment, we'll trust the
   biologists' model intuition and use log units.

2. Do an exploratory data analysis of BodyMass, TestesMass, BrainMass,
   and NeoCortexVolume.  Describe and provide a possibe explanation
   for the correlations that you see.  Neocortical volume is often
   used as an indicator for higher cognitive function.  How well
   correlated are BrainMass and NeoCortexVolume?

3. Compute a linear regression fit to predict TestesMass based on
   BrainMass alone, BodyMass alone, and BrainMass and BodyMass
   together (all in log units).  Summarize your findings.

4. Compute a linear regression fit to predict TestesMass and BrainMass
   based on BodyMass (all in log units).  Plot the residuals against
   FemalePromiscuity, MatingSystem, and Diet.  Summarize your
   findings.  Do these help explain the results of Problem 3?

5. In the previous problem set, we considered whether we could make
   claims about individuals given aggregate data.  Here, we are using
   measurements of an individual to make claims about populations of
   bats.  Is this reasonable?  Why or why not?