Linear Regression Slope Calculator — Formule
## Linear Regression Slope
The slope of the least-squares regression line measures the average change in y for each one-unit increase in x.
### Formula
**b1 = (n × Σxy - Σx × Σy) / (n × Σx² - (Σx)²)**
This is derived by minimizing the sum of squared residuals. A positive slope indicates a positive relationship; negative slope indicates an inverse relationship.
The slope of the least-squares regression line measures the average change in y for each one-unit increase in x.
### Formula
**b1 = (n × Σxy - Σx × Σy) / (n × Σx² - (Σx)²)**
This is derived by minimizing the sum of squared residuals. A positive slope indicates a positive relationship; negative slope indicates an inverse relationship.
Exemple Résolu
Given n=10, Σxy=3500, Σx=150, Σy=200, Σx²=2850.
- Numerator = 10(3500) - 150(200) = 35000 - 30000 = 5000
- Denominator = 10(2850) - 150² = 28500 - 22500 = 6000
- b1 = 5000 / 6000 = 0.8333