How to tell the importance of regression coefficients when both continuous and binary features exist Let's say I have 3 features for a regression model: if_smoking, if_drinking, and body_height. The first 2 are binary, while the 3rd is continuous. I have coefficients like:
bias/y_intercept: 1.2
coefficient for if_smoking: 0.8
coefficient for if_drinking: 0.5
coefficient for body_height: 0.2
The model, therefore, should be:
y_predict = 1.2 + 0.8*if_smoking + 0.5*if_drinking + 0.2*body_height
I can say that if_smoking is more important than if_drinking since the former's coefficient is 0.8 over the latter's 0.5, and both are binary (0 or 1).
However, is body_height more or less important than if_smoking and if_drinking? If I look at the coefficient, it's 0.2, less than if_smoking's 0.8 and if_drinking's 0.5. However, body_height is continuous. Let's say a person's height is 5 feet, 0.2*5 is greater than if_smoking's 0.8*1 and if_drinking's 0.5*1. In other words, body_height's coefficient (0.2) is smaller but its overall contribution (0.2*5=1) is larger.
So, do I say body_height is less or more important than if_smoking and if_drinking?

I presume that with "importance" you have something similar to the effect size of the various independent variables (IV) in mind. I.e. you wonder how large the change in the dependent variable (DV) y_predict is when changing one of the IVs by "a unit".
Then, the fitted coefficient of an IV tells you how much y_predict changes by changing the IV by one unit, and keeping all the other IVs fixed. E.g., if you change the IV if_smoking from zero to one and keep all the other IVs fixed, the DV y_predict will on average increase by 0.8.
Similarly, the coefficient 0.2 of body_height means that an increase in body height by one unit, i.e. one foot, would lead to y_predict increasing by 0.2. But the unit foot is quite huge for body height. A more reasonable change of e.g. 0.1 feet would result in an average change of y_predict of only 0.02. Thus, I would argue that the body height is, in comparison to the other IVs, not very "important", i.e. doesn't have as large an effect on y_predict.
Summary: Always mind your units. The coefficients can only be interpreted with the units in mind. If you had e.g. used the unit millimeter, the coefficient would have increased to 60.96, for exactly the same data and thus the same "importance" (effect).
