Logistic regression

Logistic regression is generalized linear model.

Why is logistic regression considered a linear model?
Logistic regression is considered a generalized linear model because the outcome always depends on the sum of the inputs and weights. Or in other words, the output cannot depend on the product of its parameters(weights/coefficients).
Logistic regression uses the general linear equation Y=b0+∑(biXi)+ϵY=b0+∑(biXi)+ϵ. In linear regression Y is a continuous dependent variable, but in logistic regression it is regressing for the probability of a categorical outcome (for example 0 and 1).
The net input function is simply the dot product of our input features and the respective model coefficients.

In logistic regression, the output is related to the predictors via the logistic sigmoid function.

Model: (Predictions)=Sigmoid(wTx)
After predictions,Log_likelihood is calculated.Error can be minimized by gradient descent algorithm.

In logistic regression, the outcome (dependent variable) has only a limited number of possible values.

The dependent variable:
Logistic regression is used when the response variable is categorical in nature. For instance, yes/no, true/false, red/green/blue, 1st/2nd/3rd/4th, etc.

Logistic regression gives an equation which is of the form Y = eX /(1+ eX)

In logistic regression, depends on the family (binomial, Poisson, etc.) and link (log, logit, inverse-log, etc.) you use, the interpretation is different.

Error minimization technique:
1.Logistic regression uses maximum likelihood method to arrive at the solution.
2.Error can be minimized by gradient descent algorithm also.