Logistic regression is used to predict the binary outcome from the given set of continuous predictor variables.

**Logistic regression** is **used** to obtain odds ratio in the presence of more than one explanatory variable. The procedure is quite similar to multiple linear **regression**, with the exception that the response variable is binomial. The result is the impact of each variable on the odds ratio of the observed event of interest. **Logistic regression**, also known as **logit regression** or **logit** model, is a mathematical model used in statistics to estimate (guess) the probability of an event occurring having been given some previous data. **Logistic regression** works with binary data, where either the event happens (1) or the event does not happen (0).

**Logistic regression** is a supervised classification algorithm. It is a discriminative algorithm, meaning it tries to find boundaries between two classes. It models the probabilities of one class.

In linear regression (y=mx + c) our output(y) can be from -inf to +inf , but in logistic we want our output to be probabilities ( between 0 to 1 ).

Here comes the logistic function(sigmoid function), y = 1/(1+e^(-x))

Output of linear regression:

Output of logistic regression(sigmoid curve):

The equation for simple logistic regression is:

y = e^(mx+c)/(1 + e^(mx+c))

The loss function used in logistic regression is log loss

log_loss = $\sum_{i=0}^{n} (-y_i*log(y_i’)) - (1-y_i)*(log(1-y_i’)))$

here, n is the number of training instances, y is the actual value and y’ is the predicted value.