# Transforming data

If I want to make a regression model where sales in billions are dependent variable and my independent variables consist of very low values, for example rainy days (highest number is 15). My question is, is there any problem if I do a regression with original data, or should I do some transformation and therefore make my variables comparable? And which transformation would you suggest? Is sensible to use logarithmic transformation of data here?

I tried to find similar discussion, but struggled to do it.

• As @mdewey wisely answers, the coefficients do the scaling but as a matter of practicality changing units to get coefficients closer to 1 is often a good idea. But your description to me raises a more fundamental question. Sales can't be negative, presumably, but they could be highly skewed. For that reason alone I'd expect Poisson regression (or the same beast under any other name) to be a better bet. For more on why, one way in is blog.stata.com/2011/08/22/… (That sales are measured not counted is not crucial!) Dec 1, 2016 at 11:01
• as @NickCox suggests, sales can be highly - I would add positively - skewed. So a log transformation may be better choice, as it scales the response and may make it look more symmetric. Dec 1, 2016 at 11:06
• Poisson regression arguably has all the advantages of logarithmic transformation and none of the disadvantages. Note that predictions are automatically of sales, not of log sales. Dec 1, 2016 at 11:17
• Those are good points @NickCox, I had assumed that sales were in some currency unit. I will update my answer to clarify. Dec 1, 2016 at 13:14
• @mdewey My guess is the same as yours, that sales may be in currency units and they could then be regarded as counts of whatever the smallest currency unit is. Whether they behave as counts are expected to behave (according to some model) can only be checked with access to the data! Dec 1, 2016 at 13:20