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I am looking for differences between two products A and B and I want to see whether there are significant differences on seven characteristics. For this I use a logistic regression where my dependent variable is the conditional probability of a product being B represented by π , with seven covariates that are captured by dummy variables and represented by the vector β.

π=F(x'β)

When I look at individual frequencies for each characteristic for each product, product B has a higher frequency for all characteristics than product A. Intuitively therefore it seems that on running the logistic regression the coefficients will be positive (if significant) or the odds ratio will be higher than 1. I am getting significantly positive coefficients for 4 characteristics, whereas for two there is no significance yet the coefficient is positive, and for the last one I am getting a negative coefficient that is significant. To me the last negative coefficient does not make sense as I mentioned earlier my frequencies for all characteristics are higher for product B, whereas a negative coefficient would imply that the odds of having this characteristic in product A is higher than product B.I checked for multicollinearity issues and my vif for all covariates are less than 10.

How can I justify the last negative significant coefficient despite not being an intuitive result? Or anything else that I need to check. Thanks!

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These data have the property you mention: "for each product, product B has a higher frequency for all characteristics than product A"

product x1 x2
B       1  1
B       1  1
B       1  1
B       1  0
A       0  0
A       0  1
A       0  1

But a good logistic regressor for class B is 2*x1-x2. The negative term helps predict in two of the negative cases.

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