Explain what is logistic regression?

Logistic regression is a statistical method used for binary classification tasks, where the goal is to predict the probability of a certain event happening or not happening. Despite its name, logistic regression is actually a classification algorithm rather than a regression algorithm.

Here’s how logistic regression works:

1. Sigmoid Function: Logistic regression models the probability that a given input belongs to a certain class using the logistic function, also known as the sigmoid function. The sigmoid function maps any real-valued number to a value between 0 and 1. It looks like this:

   The formula for the sigmoid function is:

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   σ(z) = 1 / (1 + e^(-z))


   Where z is the linear combination of the input features and their corresponding weights.

2. Linear Combination: In logistic regression, the linear combination z of input features (X) and weights (β) is calculated as follows:
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   z = β₀ + β₁*X₁ + β₂*X₂ + ... + βᵣ*Xᵣ


   Where:

   • z is the log-odds (logarithm of the odds) of the probability of the event occurring.
   • β₀ is the intercept term.
   • βᵢ are the coefficients (weights) associated with each feature Xᵢ.
3. Training: The logistic regression model is trained using a method such as maximum likelihood estimation. During training, the model adjusts the weights to minimize the error between the predicted probabilities and the actual class labels in the training data.
4. Decision Boundary: Once trained, the logistic regression model can be used to predict the probability that a new input belongs to the positive class (usually labeled as 1). By choosing a threshold (often 0.5), predictions can be made by comparing the predicted probabilities to this threshold. For example, if the predicted probability is greater than 0.5, the model predicts the positive class; otherwise, it predicts the negative class.

Logistic regression is widely used in various fields such as healthcare, finance, and marketing for tasks like predicting whether a customer will churn, whether an email is spam, or whether a patient has a particular disease. It’s popular due to its simplicity, interpretability, and effectiveness for binary classification problems.