**Hypothesis function**

**Logistic regression** is used for classification tasks, that predict discrete values as a result.

If you consider a binary classification problem, then the hypothesis function is bounded between [0, 1]

**Logistic regression formula: **

**Cost function**

The cost function represents the optimization objective.

The cost function could be the mean of the Euclidean distance between the hypothesis *h_θ(x)* and the actual value *y* among all them samples in the training set, when the hypothesis function is formed using the sigmoid function, this term **would result in a non-convex cost function**, which means that a local minimum can be easily located before reaching the global minimum. The cost function is convex, **it is transformed using the logarithm of the sigmoid function**.

In this way, the optimization objective function can be defined as the mean of the costs/errors in the training set:

Hope this answer helps.