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Linear Regression: Ordinary Least Squares (OLS)
Slope, intercept, residuals, Mean Squared Error, and R² score
Linear Regression models the linear relationship between continuous dependent variables and one or more independent predictor features by minimizing the sum of squared residuals.
The Linear Equation & Performance Metrics
Model equation: y_pred = w1*x1 + w2*x2 + ... + b.
Mean Squared Error (MSE): Measures average squared difference between predictions and actual values: MSE = (1/n) * Σ(y - y_pred)^2.
R² Score (Coefficient of Determination): The proportion of variance in y explained by features X (1.0 = perfect model, 0.0 = baseline mean predictor).
from sklearn.linear_model import LinearRegression
from sklearn.metrics import mean_squared_error, r2_score
import numpy as np
X = np.array([[1], [2], [3], [4], [5]])
y = np.array([2.1, 3.9, 6.2, 7.8, 10.1])
model = LinearRegression()
model.fit(X, y)
predictions = model.predict(X)
print(f"Slope (w): {model.coef_[0]:.3f}")
print(f"Intercept (b): {model.intercept_:.3f}")
print(f"MSE: {mean_squared_error(y, predictions):.4f}")
print(f"R² Score: {r2_score(y, predictions):.4f}")Set your Publisher ID in src/config/ads.ts to display live ads.
Test Yourself With Exercise
What does an R² (R-squared) score of 0.85 indicate for a linear regression model?