# Multiple regression of variables with different units

I'm new in statistical modelling and using R, so please excuse my mistake for this question.

I want to make multiple regression model with these variables:

1. Revenue (in million USD) as dependent variable
2. Customer experience score (with scale 1 to 5) as independent variable
3. Number of package return (in unit) as independent variable

Since they have different unit and the variation is quite big, I'm thinking about standardize the variables before perform the regression. Is it will be better to model with standardize variable or do regression directly? I also read from the following source about how to rescale it with R.

Standardize data columns in R

But how to interpret the model if the variables are rescaled and no longer has a certain unit?

• Hey Shawn. This question is better posed for StackExchange's "Cross Validated" site which is about statistics rather than this "StackOverflow" site which is for programming questions, so I'm going to vote to close it. However, the short answer to your question is that if you scale a variable up by, say, 7 then the estimated coefficient will be scaled by 1/7th. In linear regression, beta is the expected change in y for a one unit change in x, whatever that unit might be. So it doesn't matter what scale you "put in" the regression, as long as you know how to interpret it. Hope this helps. – DanY Feb 20 '19 at 7:39
• It is enough for you only to scale revenue which I suppose have the largest variation? Maybe you can use log(revenue) which is easier to interpret. – LocoGris Feb 20 '19 at 9:59
• Possible duplicate of What algorithms need feature scaling, beside from SVM? – kjetil b halvorsen Feb 20 '19 at 22:31

## 1 Answer

Is it will be better to model with standardize variable or do regression directly?

In this case it makes no difference, and the latter (doing regression directly) is probably better, insofar as it is simpler. If you perform a regression directly then you have the advantage that the coefficient estimates will refer to estimated slopes relating the variables on the scale of the units you are using. If you standardise the variables first then the only effect will be to alter the coefficients onto a different scale that measures the slopes relating the standardised variables. It is possible to transition between one form and the other by simple algebra, but the latter form is probably less useful for you.