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Logistic Regression Formula

Step-by-step probability calculations

1. Input Parameters (মান বসান)

β₀ (Intercept)

β₁ (Coefficient)

X (Feature Value)

Class 1 Label (Probability ≥ 0.5)

Class 0 Label (Probability < 0.5)

Step 1: Logistic Regression Formula ব্যবহার করবো

Logistic regression মূলত কোনো ঘটনা ঘটার সম্ভাবনা (probability) বের করতে ব্যবহার করা হয়।

P(Y=1) = 11 + e^{-(β₀ + β₁X)}

💡 Formula Components (উপাদানসমূহ):

X = input feature (independent variable)
β₀ = intercept parameter (bias term)
β₁ = coefficient parameter (slope)
e = mathematical constant (~2.718)

Step 2: Linear Combination (z) বের করি

💡 ধাপ ১: প্রথমে z = β₀ + β₁X এর মান বের করতে হবে।

z = -3 + (0.05 × 100)

z = -3 + 5

z = 2

Step 3: Probability (P) ক্যালকুলেট করি

💡 ধাপ ২: Sigmoid function এ বসাই।

P = 1 / (1 + e^-(2))

P = 1 / (1 + 0.135335)

P = 0.880797

Final Prediction

0.88

Predicted Probability

Chance of churn

Decision Rule

Probability ≥ 0.5 → Churn

Probability < 0.5 → No Churn

Result

Since 0.88 ≥ 0.5, we predict:

→ Churn

Logistic Regression in real-world business

Logistic Regression predicts probability for a binary outcome (0 or 1). The model builds a linear score z = β₀ + β₁X, then converts that score into probability using the sigmoid function: p = 1 / (1 + e⁻ᶻ). This guarantees p stays between 0 and 1.

Business students use logistic regression for churn prediction, loan default risk, campaign response prediction, fraud flagging, and lead qualification. A threshold of 0.5 is commonly used, but in business settings this can be adjusted based on cost tradeoffs.