A look at transformations in the context of simple linear regression. I look at two examples where taking a transformation (applying a function to the response and/or explanatory variables) can help to satisfy the assumptions of the simple linear regression model.

The brain and body weight data is from:

Sacher, G.A. Staffeldt, E. (1974). Relation of gestation time to brain weight for placental mammals: Implications for the theory of vertebrate growth. The American Naturalist, 108:593–615. The 99 observations represent one pair of measurements for each of the 99 species that had a brain and body weight measurement.

The hardness-density data is found in:

Hand, D.J., Daly, F. , Lunn, A.D., McConway, K., and Ostrowski, E., editors (1994). The Handbook of Small Data Sets. Chapman & Hall, London.

Original source: Williams, E.J. (1959). Regression Analysis. John Wiley & Sons, New York. Page 43, Table 3.7.