What is the Normal Equation in Linear Regression?
Updated May 16, 2026
Short answer
The Normal Equation provides a closed-form solution to compute optimal linear regression parameters without iterative optimization.
Deep explanation
Instead of using gradient descent, linear regression can be solved analytically using θ = (XᵀX)⁻¹Xᵀy. This minimizes the mean squared error directly. It is efficient for small datasets but becomes computationally expensive when features are large due to matrix inversion complexity.
Real-world example
Used in small-scale financial datasets where quick exact solutions are needed.
Common mistakes
- Applying normal equation on large datasets without considering computational cost or singular matrices.
Follow-up questions
- What happens if XᵀX is not invertible?
- Why is gradient descent preferred in big data?