Multiple Regression Calculator
Fit a multiple linear regression y = b₀ + b₁x₁ + b₂x₂ for two predictors using normal equations.
About Multiple Regression Calculator
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
Worked example
With the default values below, Multiple Regression Calculator returns Intercept (b₀) of 1.300000. Change any input above and every figure here is recalculated in your browser.
Inputs 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
Results
- Intercept (b₀)
- 1.300000
- Coefficient b₁
- 0.333333
- Coefficient b₂
- 1.833333
- R²
- 0.993304
Step by step
- 1Values used
- 2Formula applied
- 3Intercept (b₀)= 1.300000
- 4Coefficient b₁= 0.333333
- 5Coefficient b₂= 1.833333
- 6R²= 0.993304
Assumptions and limits
- The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
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|.