What is logistic regression?

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🔹 What is Logistic Regression?

Logistic Regression is a supervised machine learning algorithm used for classification problems. Unlike linear regression (which predicts continuous values), logistic regression predicts categorical outcomes — usually binary (e.g., Yes/No, Spam/Not Spam, Disease/No Disease).

It is called “regression” because it uses a linear combination of input features, but instead of directly outputting values, it applies a logistic (sigmoid) function to map results between 0 and 1.

🔹 How it Works

1. Input features are combined linearly:

   $$z = w_0 + w_1x_1 + w_2x_2 + ... + w_nx_n$$

2. Apply the sigmoid function to squash the output between 0 and 1:

   $$\sigma(z) = \frac{1}{1 + e^{-z}}$$

   • If output > 0.5 → Predict Class 1

   • If output ≤ 0.5 → Predict Class 0

🔹 Example

Suppose you want to predict whether a student passes (1) or fails (0) based on study hours.

• Linear equation:

  $$z = -3 + 1.2 \times (\text{hours studied})$$

• Sigmoid output gives the probability of passing.

  • If probability = 0.85 → Predict Pass

  • If probability = 0.2 → Predict Fail

🔹 Applications

• Email classification (Spam vs. Not Spam).

• Medical diagnosis (Disease vs. No Disease).

• Fraud detection (Fraudulent vs. Genuine transaction).

• Customer churn prediction (Leave vs. Stay).

🔹 Key Points

• Logistic regression is for classification, not regression.

• It outputs probabilities (between 0 and 1).

• Uses the sigmoid function to map values.

• Decision boundary is based on a threshold (commonly 0.5).

✅ In short: Logistic regression is a simple yet powerful algorithm that predicts probabilities and classifies data into categories.

Read more :

Explain linear regression

What are features and labels in ML?

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