Linear relations are commonplace in science and data analysis. Obviously, linear models are easier to understand than non-linear models. So historically, tools for linear models were developed first. In certain cases, it pays to linearize (make linear) data to make analysis simpler. A simple strategy that sometimes works is to square or cube one or more variables. Similarly, we can transform the data down an imaginary power ladder by taking the square or cube root.
In this recipe, we will use data from the Duncan dataset as described in https://vincentarelbundock.github.io/Rdatasets/doc/car/Duncan.html (retrieved August 2015). The data was gathered around 1961 and is about 45 occupations with four columns—type, income, education, and prestige. We will take a look at income and prestige. These variables seem to be linked by a cubic polynomial, so we can take the cube root of income or the cube of prestige. To check the result, we will visualize the residuals...