Logistic Regression Model

Why logistic regression?
In the field of medicine, we often encounter such data: disease and non disease, survival and death, negative and positive These results are binary variables. If we want to study the relationship between independent variables and categorical dependent variables, it is useless to use multiple linear regression model, because multiple linear regression model studies continuous dependent variables and requires the distribution type of population (dependent variable) to be normal distribution. Therefore, when the dependent variable is classified variable, logistic regression model should be used.
What is logistic regression model?
logit transformation 
When we establish the regression equation, the value range of dependent variables is the real number set; however, in the problem we studied, the values of these categorical dependent variables are between 0 and 1, such as the prevalence rate of 0.1, 0.5, 0.8, etc., so we need to do logit transformation on the value of dependent variable (target probability).
If the probability of event occurrence is p and the probability of non occurrence is 1 − P, then P1 − P is called the occurrence ratio of events, which is recorded as odd (ratio and advantage). Logit transformation is as follows:
logit(p)=ln(p1−p)
Obviously, when p = 1, logit (P) is + ∞; when p = 0.5, logit (P) = 0; when p = 0, logit (P) is − ∞. In this way, the value range of dependent variable is extended from 0 ~ 1 to real number set, and the regression analysis using this treatment is logistic regression.
Logistic regression model
There is a dichotomous dependent variable y, when the value is 1, the event occurs, when the value is 0, the event does not occur; the dependent variable has m influencing factors (independent variables): x1, X2,..., XM; if the conditional probability of event occurrence P (y = 1 ∣ Xi) = Pi, the logistic regression model constructed by pi (the i-th observation) is as follows:
logit(pi)=ln(pi1−pi)=β0+β1x1+⋯+βmxm=β0+∑j=1mβjxj,j=1,2,⋯,m
Where β J represents the change of Logit (PI) when the independent variable XJ changes by one unit, which can be understood as the weight coefficient of each influencing factor.
Through transformation, logistic regression model can also be written as follows:
pi=eβ0+∑mj=1βjxj1+eβ0+∑mj=1βjxj
By observing the logistic regression model, we can find that it is very similar to the linear regression model. In fact, logistic regression model belongs to generalized linear model.