Larger animals tend to have larger brains. But is the increase in brain size proportional to the increase in body size? A set of data on body and brain size of 62 mammal species was collated by Allison and Cicchetti (1976), and these data are in the data set "mammals.csv". The file contains columns giving the species name, the average body mass (in kg) and average brain size (in g) for each species.

a. Plot brain size against body size. Is the relationship linear?

b. Find a transformation (for either or both variables) that makes the relationship between these two variables linear.

c. Is there statistical evidence that brain size is correlated with body size? Assume that the species data are independent.

d. What line best predicts (transformed) brain size from (transformed) body size?

e. Based on your answer in (d), what is the predicted change in log-brain size accompanying an increase of 3 units of log- body size? f. Make a residual plot using the regression fitted to the transformed variables. Do the data look like they match the assumptions of linear regression?

g. Which species has the highest brain size relative to that predicted by its body size? Which species has the smallest brain relative to that predicted by its body size?