Logistic regression

Introduction to Logistic Regression

When you hear the term "logistic regression", you might think it’s just another type of regression, like linear regression. But in reality, it’s more about classification than predicting continuous values.

Logistic regression is one of the most widely used algorithms in machine learning, especially when the target variable is binary (two possible outcomes).

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When to Use Logistic Regression

Logistic regression is used when the output you’re trying to predict has only two possibilities, such as:

• Spam vs. Not Spam

• Pass vs. Fail

• Customer will Buy vs. Won’t Buy

If your data fits into categories like Yes/No, 0/1, or True/False, logistic regression is a great starting point.

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Why Not Just Use Linear Regression?

With linear regression, the output can be any number from negative infinity to positive infinity.
That doesn’t work for classification, because probabilities must be between 0 and 1.

Example:
If you’re predicting whether it will rain tomorrow, a model saying probability = 1.7 or -0.3 makes no sense.

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The Logistic Function (Sigmoid)

To keep predictions between 0 and 1, logistic regression uses the sigmoid function:

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

Where:

• $z$ = the linear combination of inputs (just like in linear regression)

• $\sigma(z)$ = probability output between 0 and 1

Example:

• If $z = 0$ → output = 0.5 (50% probability)

• If $z$ is very large → output ≈ 1 (almost certain)

• If $z$ is very negative → output ≈ 0 (almost impossible)

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How Logistic Regression Works

1. Linear Step: Calculate $z = w_1x_1 + w_2x_2 + ... + b$

2. Sigmoid Step: Convert $z$ into a probability using the sigmoid function.

3. Classification Step:

   • If probability ≥ 0.5 → Predict class 1

   • If probability < 0.5 → Predict class 0

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Decision Boundary

Logistic regression draws a line (or hyperplane) that separates classes in the feature space.
Everything on one side is classified as 1, and everything on the other as 0.

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Why Logistic Regression is Popular

• Simple to implement

• Works well with small datasets

• Provides probabilities, not just classifications

• Easy to interpret coefficients

• Fast to train

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In short: Logistic regression is your go-to algorithm for binary classification problems. It’s simple, powerful, and a great foundation before moving into more complex models like decision trees or neural networks.

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I can also create a visual diagram for your blog showing:

1. A sigmoid curve

2. A decision boundary on a scatter plot

3. How probabilities map to predictions

That would make this intro post more engaging. Do you want me to prepare that?