Why it’s called “regression”

Logistic regression is a classification algorithm.

It models a probability using a logistic (sigmoid) function.

Binary logistic regression

It predicts:

• probability of class 1, p = P(y=1|X)p = P(y=1|X)

Then:

• predict 1 if p >= thresholdp >= threshold else 0

  flowchart LR
  Z[Linear score z = w·x + b] --> S[Sigmoid]
  S --> P[p = probability]
  P --> Y[Class via threshold]

The sigmoid intuition

• large positive z → p close to 1
• large negative z → p close to 0

Multiclass logistic regression

Common approaches:

• One-vs-Rest (OvR): train one classifier per class
• Softmax (multinomial): one model for all classes

Scikit-learn can do both.

Scikit-learn example

from sklearn.linear_model import LogisticRegression
 
# For multiclass, common choice:
clf = LogisticRegression(max_iter=1000, multi_class="auto")

from sklearn.linear_model import LogisticRegression
 
# For multiclass, common choice:
clf = LogisticRegression(max_iter=1000, multi_class="auto")

Threshold tuning matters

Default threshold is 0.5, but for imbalanced problems you may choose:

• lower threshold to increase recall
• higher threshold to increase precision

Mini-checkpoint

If missing fraud is expensive, do you optimize for precision or recall?

(Usually recall.)

🧪 Try It Yourself

Exercise 1 – Train-Test Split

Exercise 2 – Fit a Linear Model

Exercise 3 – Evaluate with MSE