Non-linear effects with log transformation

The video discusses regression analysis, emphasizing its limitation in only addressing linear relationships between a dependent variable and one or more independent variables. It introduces the log transformation as a method to deal with nonlinear relationships. For example, it's common in research to use the logarithm of a variable like revenue when the data is highly skewed. The transformation not only addresses skewness but also changes the scale of measurement from absolute to relative units, which is more meaningful in certain contexts, like comparing percentage growth.

The video further illustrates the application of log transformation through a case study of the largest 500 Finnish companies in 2005, highlighting how the logarithmic scale more effectively represents their revenue distribution. It then delves into a regression analysis example using the Prestige data set from the Canadian census, where the income of various occupations is analyzed in relation to their prestige score. The log transformation here helps in fitting a non-linear model, better capturing the essence of the data. The video concludes with methods of interpreting log-transformed regression results, either through marginal prediction plots or direct interpretation, where a unit increase in the independent variable reflects a percentage change in the dependent variable, facilitating a more intuitive understanding of exponential growth models.

Slides: https://osf.io/w39hg