The model

Multiple linear regression uses multiple features:

ŷ = w1·x1 + w2·x2 + ... + wk·xk + bŷ = w1·x1 + w2·x2 + ... + wk·xk + b

  flowchart LR
  X1[x1] --> M[Linear Model]
  X2[x2] --> M
  Xk[xk] --> M
  M --> Y[Prediction ŷ]

Interpreting coefficients

If all else is equal:

• wkwk tells how much the target changes when feature xkxk increases by 1.

But be careful:

• if features are correlated, coefficient interpretation becomes tricky (multicollinearity)

Scikit-learn example

import numpy as np
from sklearn.linear_model import LinearRegression
 
# Example: [size_sqft, bedrooms, age]
X = np.array([
    [800, 2, 10],
    [1000, 3, 5],
    [1200, 3, 20],
    [1500, 4, 7],
])
 
y = np.array([180, 240, 220, 320])
 
model = LinearRegression()
model.fit(X, y)
print("coefficients:", model.coef_)
print("intercept:", model.intercept_)

import numpy as np
from sklearn.linear_model import LinearRegression
 
# Example: [size_sqft, bedrooms, age]
X = np.array([
    [800, 2, 10],
    [1000, 3, 5],
    [1200, 3, 20],
    [1500, 4, 7],
])
 
y = np.array([180, 240, 220, 320])
 
model = LinearRegression()
model.fit(X, y)
print("coefficients:", model.coef_)
print("intercept:", model.intercept_)

Common issues

• multicollinearity: features carry overlapping signal
• scaling: if using regularization, scale inputs

Mini-checkpoint

• Which features are strongly correlated?
• Consider removing or combining them (feature engineering) if needed.

🧪 Try It Yourself

Exercise 1 – Train-Test Split

Exercise 2 – Fit a Linear Model

Exercise 3 – Evaluate with MSE