Linear Regressions Slope Rechner — Formel
## How to Calculate the Regression Slope
### Formula
**b1 = [n*Sum(xy) - Sum(x)*Sum(y)] / [n*Sum(x^2) - (Sum(x))^2]**
The slope of the least-squares regression line represents the predicted change in Y for a one-unit increase in X. A positive slope indicates a positive relationship; negative means Y decreases as X increases.
### Formula
**b1 = [n*Sum(xy) - Sum(x)*Sum(y)] / [n*Sum(x^2) - (Sum(x))^2]**
The slope of the least-squares regression line represents the predicted change in Y for a one-unit increase in X. A positive slope indicates a positive relationship; negative means Y decreases as X increases.
Lösungsbeispiel
n = 5, Sum(xy) = 2350, Sum(x) = 75, Sum(y) = 150, Sum(x^2) = 1175.
- Numerator = 5*2350 - 75*150 = 11750 - 11250 = 500
- Denominator = 5*1175 - 75^2 = 5875 - 5625 = 250
- Slope b1 = 500 / 250 = 2.0
- For each unit increase in x, y increases by 2 on average