Linear regression
- Machine Learning course
- Beginner
- Lesson 42/112
- 5 min
Linear regression finds the linear relationship in data and fits a line.
Fitting a line
Linear regression fits the line y = w·x + b to the data. w is the slope, b the intercept. With several features each feature has its own weight: y = w₁x₁ + w₂x₂ + ... + b.
m = LinearRegression().fit([[1], [2], [3]], [2, 4, 6])
print(m.coef_) # [2.]
print(m.intercept_) # 0.0 (approximately)The weights are interpretable: w = 2 says y rises by two units when x rises by one.
Least squares
The "best" line is the one that minimises the sum of squared prediction errors. Squaring both equalises negative and positive errors and penalises large errors more.
x = np.array([1, 2, 3, 4])
y = np.array([2.1, 3.9, 6.2, 7.8])
w, b = np.polyfit(x, y, 1) # degree 1: a line
print(round(w, 2), round(b, 2)) # 1.94 0.15np.polyfit and LinearRegression find the same least-squares solution.
Practice Slope and intercept
Train a LinearRegression with the two-feature X. Round coef_ and intercept_ with np.round(..., 2) and print them on separate lines.
Starter code
import numpy as np
from sklearn.linear_model import LinearRegression
X = np.array([[1, 0], [0, 1], [1, 1], [2, 1]])
y = 3 * X[:, 0] + 2 * X[:, 1] + 5
# buraya yazSample solution
import numpy as np
from sklearn.linear_model import LinearRegression
X = np.array([[1, 0], [0, 1], [1, 1], [2, 1]])
y = 3 * X[:, 0] + 2 * X[:, 1] + 5
m = LinearRegression().fit(X, y)
print(np.round(m.coef_, 2))
print(np.round(m.intercept_, 2))Expected output
[3. 2.] 5.0
Questions and answers
Review the lesson questions together with their answers. To test yourself, solve the lesson interactively.
1 In a house model, what does a square-metre weight of 15 mean?
- The price is 15 units
- 15 m² houses are the most expensive
- The model is 15 percent wrong
- Each extra m² raises the price by 15 units Correct answer
Explanation: The weight is the one-unit effect of that feature with the others held fixed.
2 Read the learned slope.
egim = m.____[0]egim = m.coef_[0]Explanation: coef_ is an array holding one weight per feature.
3 Match the terms.
| Term | Meaning |
|---|---|
w |
Slope (weight) |
b |
Intercept |
least squares |
Minimising squared error sum |
np.polyfit |
Polynomial fitting |