Going over an example of Regression model specification and looking for some clarity on a statement they gave for an example: Its concluded that market cap is not linearly related to P/E, but the natural log of market cap is linearly related to P/E… What exactly does that mean when market cap itself is not linearly related but the natural log is??
It means market cap and P/E do not share a linear relationship and a regression equation would have poor explanatory power. However, if you look at a graph of the results, it may resemble a curve that is continuously growing, which indicates a log-linear relationship. If you take the natural log of the original regression equation and plot the results, it should resemble a linear relationship.
What are some other examples of log-linear relationships in finance other than market cap and P/E?