Illuminating Statistical Analysis Using Scenarios and Simulations

53Transforming the Scale of Scaled Data

Heavily skewed distributions are actually somewhat common in some contexts. For example, income across households as well as gross domestic product (GDP) per capita across countries are not normally distributed. Such distributions are heavily skewed to the right (positively skewed). In the case of household income, for example, the income of a large majority of households falls between zero and, say, $75,000 and a minority of richer households are spread out all the way to who knows how much. Economists typically transform such values by taking their (natural) logarithms, which helps to normalize skewed data distributions. They can then use the transformed values in their linear regression models.

Logarithmic and exponential functions are inverses of each other; they undo each other. For example: and ; and ; and ; and so on. When taking logs, the ...