The logistic regression is given by –

πi=Pr(Yi=1|Xi=xi)=exp(β0+β1xi)1+exp(β0+β1xi)

The coefficient formula for logistic regression, also known as the logistic function or sigmoid function, is as follows:

$P (y = 1∣ x) = 1 + e ^{- (β 0 + β 1 x 1 + β 2 x 2 + \dots + β n x n)} 1$

Where:

$P (y = 1∣ x)$ is the probability that the dependent variable $y$ equals 1 given the independent variables $x_{1}, x_{2}, \dots, x_{n}$ .
$β_{0}, β_{1}, \dots, β_{n}$ are the coefficients or parameters of the logistic regression model, representing the relationship between the independent variables and the log-odds of the dependent variable.
$e$ is the base of the natural logarithm.

This formula calculates the probability of a binary outcome (usually coded as 0 or 1) given the values of the independent variables. The logistic function ensures that the predicted probabilities lie between 0 and 1, making it suitable for binary classification problems.