# How to interpret coefficients relative to one another (regression) continuous and binary

I have a mix of continuous and binary data. promotion here is binary so 1= yes 0=no. i standardize (mean 0 and s.d. 1 ) the continuous variables so they are same unit.

I get the following output: is this the correct interpretation?

• a one unit s.d increase in temperature increase the s.d in products sold by 1030 therefore it has a large affect ; if we compare this to costs, costs has a greater coeff than temperature and therefore is more important
• for binary : if we run a promotion we can expect an increase in 5727 units sold.
• since coeff is greater for promotion than any others it is much more important feature : this one i struggle with, since the data for binary is not standardized and the coefficient has a different meaning is it right to compare relative importance between binary and continuous -- if not how can i RANK the predictors against one another?

You shouldn't compare continuous and binary features without a transformation. In this situation (because promotion seems to be important) I would make the continuous variables into binary variables by assigning a 1 or 0 based on the range, for example:

Temperature between 0-32: 1 or 0 Temperature between 33-70: 1 or 0 Temperature between 70-90: 1 or 0 Temperature above 90: 1 or 0

Now you have four new binary features that represent temperature. You can now run a regression model and safely compare the coefficients with "promotion." Do the same for costs.

Caution: don't add too many binary features! For regression you should try and keep the number of coefficients under 10. If you add too many coefficients it will artificially inflate your R^2 value.

• -1 There is no issue mixing continuous and binary variables in a regression. ANCOVA with two groups is one example. Further, binning data like this loses information. It says that 32 and 33 are less alike than 70 and 33. – Dave Feb 9 at 23:56
• Dave my mistake on mixing the variables, thanks for the correction. Binning can be helpful in this case, but you are right there is a trade-off. The ranges I picked are pretty arbitrary I leave it up to Maths12 to find the best ones. – bstrain Feb 10 at 1:59
• How do you figure that the binning helps in this case? – Dave Feb 10 at 2:09
• If you bin and run regression you can learn if temp's effect changes over its range. – bstrain Feb 10 at 2:14
• Robert Long and others on here have addressed that on here and how splines are superior if you’re concerned that temperature should have a nonlinear term. – Dave Feb 10 at 2:19