Regression Space
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Linear Regression
Linear regression fits a straight line y = mx + b to data by minimizing
the sum of squared residuals. It is the foundation of many ML algorithms.
How to Use
- Click canvas to add data points
- Choose a dataset preset to explore patterns
- Press Fit to compute the best-fit line
- Switch to Gradient Descent to animate training
- Toggle residuals to see error distances
Normal Equation
The closed-form solution computes optimal parameters directly:
w = (XTX)-1XTy
Solves in one step, no iteration needed.
Gradient Descent
Iteratively updates parameters by following the gradient:
w ← w − η · ∂L/∂w
Where η is the learning rate and L is MSE loss.
- Initialize weights randomly
- Compute predictions ŷ = Xw
- Compute loss L = (1/n)Σ(y − ŷ)²
- Compute gradient ∂L/∂w
- Update weights w ← w − η·∂L/∂w
- Repeat until convergence
Mean Squared Error
MSE = (1/n) Σᵢ (yᵢ − ŷᵢ)²
Average squared difference between actual and predicted values.
R² Score
R² = 1 − SS_res / SS_tot
Proportion of variance explained by the model. R²=1 is perfect fit.
Gradient
∂MSE/∂m = −(2/n) Σᵢ xᵢ(yᵢ − ŷᵢ)
Slope gradient — direction to update m.
∂MSE/∂b = −(2/n) Σᵢ (yᵢ − ŷᵢ)
Intercept gradient — direction to update b.
Fit Metrics
| Points | 0 |
| Slope (m) | - |
| Intercept (b) | - |
| MSE | - |
| R² | - |
| Iteration | - |
| Status | Add points to begin |