Logistic Regression

Logistic Regression

1️⃣ What is Logistic Regression?

Logistic Regression predicts the probability that an input belongs to a class.

📌 Output is always between 0 and 1

• 1 → Yes / True / Positive
• 0 → No / False / Negative

2️⃣ Where Do We Use Logistic Regression?

3️⃣ Why Not Linear Regression?

Linear regression can give values like:

-10, 1.5, 120

❌ Not suitable for classification.

Logistic Regression solves this by using the Sigmoid Function.

4️⃣ Sigmoid Function (Heart of Logistic Regression)

Formula:

σ(z) = 1 / (1 + e^(-z))

📈 It converts any value into 0 to 1.

5️⃣ How Logistic Regression Works

1️⃣ Take input features 2️⃣ Multiply by weights 3️⃣ Add bias 4️⃣ Apply sigmoid function 5️⃣ Convert probability to class

📌 Decision rule:

If probability ≥ 0.5 → Class 1
Else → Class 0

6️⃣ Simple Example (Student Pass/Fail)

📌 The model learns:

“More study hours → higher chance of passing”

7️⃣ Python Example

from sklearn.linear_model import LogisticRegression

X = [[1], [2], [3], [4], [5]]
y = [0, 0, 1, 1, 1]

model = LogisticRegression()
model.fit(X, y)

# Predict pass/fail for 2.5 hours
print(model.predict([[2.5]]))

# Predict probability
print(model.predict_proba([[2.5]]))

8️⃣ Logistic vs Linear Regression (Exam Table)

9️⃣ Advantages

✅ Simple and fast ✅ Easy to interpret ✅ Works well for binary classification ✅ Less computation

🔟 Limitations

❌ Only for binary classification ❌ Assumes linear relationship ❌ Not good for complex data

📌 Key Exam Points

• Logistic Regression uses sigmoid function
• Output is probability
• Used for classification
• Threshold usually 0.5