# Linear regression where explanatory variable of 0 has no meaning

I want to build a predictive model, where given a few numeric explanatory variable n1, n2, n3, it would predict a boolean response variable r1. I see a relationship between n1 and r1. As n1 goes up, the probability of r1 being true also goes up. For example, say the following is a representative subset of my training data (ignoring the other explanatory variables n2 and n3).

n1     r1
1  False
10  False
25  False
30  False
37   True
46   True
48  False
52  False
55   True
57  False
60   True
62  False
70   True
80   True
90   True
99   True


It seems like it'd make sense to perform logistic regression to build the predictive model, with n1 as the explanatory variable and r1 as the response variable. n1 could be a useful predictor - as it goes up from 1 to 99, the probability of r1 being true increases.

The problem is that out of my dataset, n1 of 0 does not follow the same relationship. If my model is valid, then n1 of 0 should be a strong indication that r1 is False. As it turns out from the training data, n1 of 0 has no predictive power over r1. For example, say n1 is a measurement of some kind of rate. n1 being 0 could indicate an absence of this measurement.

n1     r1
0  False
0   True
0  False
0   True
0  False
0   True


What is best way to approach this? I feel like just throwing n1 into logistic regression is not a good idea.

One way is to add a new categorical variable - valid_n1, where it is True if n1 is greater than 0, and False otherwise. I could add this new variable into the regression.

Is this a good approach? Should I go back and modify the original n1 field?

EDIT I would prefer not to remove all entries where n1 is 0, since there is a large number of them.

• Can you just remove all training data for cases where $n_1 = 0$? If not, why not? – David K Oct 13 '15 at 19:12
• @DavidK - There is a large number of training data entries where n1 is 0, so I'd prefer not to filter them out as I'd expect to see a lot of 0s in the test data too. Is there a better way than to filter them out? – user3240688 Oct 15 '15 at 4:23