Multiple Regression Calculator
Fit a multiple linear regression y = b₀ + b₁x₁ + b₂x₂ for two predictors using normal equations.
Inputs
Intercept (b₀)
1.300000
Coefficient b₁
0.333333
Coefficient b₂
1.833333
R²
0.993304
Step by step
Values used
X₁ values (comma separated) = 1, 2, 3, 4, 5; X₂ values (comma separated) = 2, 1, 4, 3, 5; Y values (comma separated) = 5, 4, 10, 8, 12
Formula applied
y = b₀ + b₁x₁ + b₂x₂, solved via (XᵀX)b = Xᵀy
Intercept (b₀)
= 1.300000
Coefficient b₁
= 0.333333
Coefficient b₂
= 1.833333
R²
= 0.993304
How it works
Multiple linear regression fits a plane y = b₀ + b₁x₁ + b₂x₂ to data with two predictors. Coefficients are found by solving the normal equations (XᵀX)b = Xᵀy.
Formula
y = b₀ + b₁x₁ + b₂x₂, solved via (XᵀX)b = Xᵀy
- b₀
- Intercept
- b₁
- Coefficient for X₁
- b₂
- Coefficient for X₂
Frequently Asked Questions
Why only two predictors?
This calculator uses a closed-form 3×3 normal equation solver for clarity and speed. For more predictors, matrix libraries or iterative methods are needed.
What does a negative coefficient mean?
A negative bᵢ means that when xᵢ increases by 1 (holding the other predictor constant), y decreases by |bᵢ|.