I want to perform a linear regression analysis. The distributions of data for all continuous variables are not normal. The tail of graph is to the right and thre highest point of graph is due to the left. (I know that in this situation we can change data by using log. (if the highest point is in the right and the tail of graph in the left ^2 could be used.) Now I think Log 10 is a better option. What about Ln or log 2? Is there a rule about the type of Log in this situation?
If you are solving a plain OLS analytically (i.e. using psuedoinverse, as in most statistical packages), then the base of the log doesn't matter since it will just be a constant multiplicative factor like @whuber mentioned.
But if you have a large dataset and solving the regression via some iterative algorithm such as stochastic gradient descent, then choosing a proper log base could help with convergence speed.
- Pick a log base such that the variance of the transformed attribute is comparable to that of other attributes
- Picking the wrong log base will still converge to the same answer eventually, it just affects convergence speed