I am working on multiple linear regression that would predict the price of the properties. I am at the stage of numerical variables transformation. I have read about standardization and various transformations like log, etc., which made me feel very confused. My numerical variables are square meters, age (in years), and number of attributes like bathrooms, rooms (they are approx. between 1-5). My questions are:

  1. The area and price variables distributions are kind of right-skewed. Would it be ok if I log transform all of them?

  2. The age variables distributions are multimodal. Are there any transformations that I can apply in this case? Should I leave them as they are or just discard them from the modeling?

  3. How should I treat the variables such the number of room, kitchens, bathrooms (they are usually low numbers 1 to 5)? wouldn't it cause any problems if the area variables are log transformed?

  4. In some articles they say that the mean and std. dev. standardization is a must for all of the numerical variables. Should I just do it instead of all of the above?