# How to measure the "Impact/influence" of a feature y on Logistic regression model based on the coefficients?

I have a dataset X which contains probabilities returned for classification 4 different classification models, say M1, M2, M3, M4 those probabilities are use to feed a fourth model M4 and that model also returns probabilities between (0, 1)

The 4 models above try to measure the probability of a customer to fall in default, and each of them measure different characteristics of customers.

So mi table X looks like:

M1 | M2| M3| M4 | y
.5 | .7|.3 | .6 | 1
.3 | .6|.2 | .7 | 0
.7 | .1|.2 | .1 | 1
.1 | .2|.4 | .1 | 0
.6 | .7|.1 | .6 | 1
.2 | .9| 0 | .5 | 0


I have another binary variable y for which I want to measure the impact of every model on y so I want to find a measure of impact /influence of each model on this variable y

What I tried so far was to run a logistic regresion on X to explain y say I obtaine the coeffients:

Intercept : -3.74587192 b1 : 4.647923 b2 : -0.354599 b3 : 2.984094 b4 : 8.983295

Q1: Haw can I find a measure of influence on y based on the Logistic regression coefficients?

Q2: Is it possible to establish a relationship of relative importance of each feature based on the coefficients?

To add to the other answer, we have $$P(Y=1|x_1,..,x_p)=sigmoid(b_0+b_1x_1+...+beta_px_p).$$ the inverse of sigmoid is log odds (aka logit).
$$log(odds(Y=1))=b_0+b_1x_1+...+b_px_p$$
and hence for coefficient $$b_i$$ you have that the log odds changes by $$b_i$$ With an increase in $$x_i$$ of one unit holding all other variables constant (which is only possible if $$x_1,...,x_p$$ are independent).
So a coefficient’s absolute magnitude dictates the effect of its corresponding feature on $$Y$$. Therefore the absolute magnitude of the coefficient is related to its importance. To some extent this answer depends on your definition of influence and of importance.