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Suppose that I'm using this function to implement logistic regression in MATLAB R2015a:

[coefs,~,stats] = glmfit(TrainInputs,TrainTargets,'binomial','logit'); % Logistic regression

I have ten continues inputs and a binary output (1 and 0). This is the coefs output of above function:

coefs = 
2.04869088486007
-4.66230054501349
0.355690380077187
-1.87230109681715
6.85763253382301
3.46437006313075
-0.282766819896174
-1.08763387246821
-1.94250600133904
1.46621342829667
-2.83661766065114

What is meaning of the coefs in logistic regression of MATLAB? Suppose that input names are X1 to X10. If we have 1 % increase in X1, We have -4.66% increase in probability of being class 1?

user2991243
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    The duplicate includes logistic regression as a special case. The first part of my answer addresses it directly. It concludes, "Thus, $\beta_m$ is the marginal change in log odds with respect to $X_m$." – whuber Jun 19 '15 at 14:27
  • @whube . Thank you for comment. for a negative value like -4.6623 we have exp(-4.6623)=0.0094. So now we have a positive value. We should consider negative sign here or positive sign? a one-unit change in the variable corresponding to "X1" will multiply the relative risk of the outcome (negative or positive?) (compared to the base outcome) by 0.0094 ? – user2991243 Jun 19 '15 at 14:58
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    Maybe that's correct--but all your parentheses and mischaracterizations get in the way of being sure of what you are saying. A relative risk cannot be negative. An exponentiated value cannot be negative. There is no meaning in "compared to the base outcome": a relative risk already involves a comparison. – whuber Jun 19 '15 at 16:05
  • Can you revise this sentence with this new negative coefficient? a one-unit change in the variable corresponding... . – user2991243 Jun 19 '15 at 16:07

1 Answers1

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The answer is no, user2991243; you can apply that interpretation in the linear regression model, while the interpretation of $\beta$ coefficient in the logistic regression model is pretty different, because of the logit transformation and the fact that $\beta$ coefficients are odds ratios and, so, not linear in the probability.

Here you can find the explanation of such transformation and the relative interpretation (using stata).

Hope this helps.

Quantopik
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  • Thank you for answer. So for example for X4 with value of 6.85763253382301 : we will see 10461% !! increase in the odds of output for a one-unit increase in x4. exp(6.85763253382301) = 951.1127 and 11%*951=10461 ?? – user2991243 Jun 19 '15 at 14:19