How to Calculate Multiple Regression Equation by Hand
Multiple regression is a statistical technique used to determine the relationship between a dependent variable and two or more independent variables. Calculating the multiple regression equation by hand is a crucial skill for understanding the underlying data and assumptions.
How to Use This Calculator
- Enter the values for X1, X2, X3, and Y.
- Enter the sample size (N).
- Click ‘Calculate’.
Formula & Methodology
The multiple regression equation is given by:
Y = b0 + b1*X1 + b2*X2 + b3*X3
Where b0, b1, b2, and b3 are the regression coefficients calculated as follows:
b1 = Σ[(X1i – X1mean) * (Yi – Ymean)] / Σ[(X1i – X1mean)²]
Real-World Examples
Data & Statistics
| X1 | X2 | X3 | Y |
|---|
| X1mean | X2mean | X3mean | Ymean |
|---|
Expert Tips
- Always check the assumptions of multiple regression before interpreting the results.
- Consider using software or calculators for large datasets to avoid errors.
Interactive FAQ
What is the difference between simple and multiple regression?
Simple regression involves only one independent variable, while multiple regression involves two or more.