Korrelations Coefficient Rechner — Formel
## How to Calculate the Pearson Correlation Coefficient
### Formula
**r = [n*Sum(xy) - Sum(x)*Sum(y)] / sqrt{[n*Sum(x^2) - (Sum(x))^2] * [n*Sum(y^2) - (Sum(y))^2]}**
The Pearson correlation coefficient measures the strength and direction of the linear relationship between two variables. It ranges from -1 (perfect negative) to +1 (perfect positive). Zero indicates no linear relationship. R-squared gives the proportion of variance explained.
### Formula
**r = [n*Sum(xy) - Sum(x)*Sum(y)] / sqrt{[n*Sum(x^2) - (Sum(x))^2] * [n*Sum(y^2) - (Sum(y))^2]}**
The Pearson correlation coefficient measures the strength and direction of the linear relationship between two variables. It ranges from -1 (perfect negative) to +1 (perfect positive). Zero indicates no linear relationship. R-squared gives the proportion of variance explained.
Lösungsbeispiel
5 data pairs with given sums: Sum(xy)=2350, Sum(x)=75, Sum(y)=150, Sum(x^2)=1175, Sum(y^2)=4650.
- Numerator = 5*2350 - 75*150 = 11750 - 11250 = 500
- Denom part 1 = 5*1175 - 75^2 = 5875 - 5625 = 250
- Denom part 2 = 5*4650 - 150^2 = 23250 - 22500 = 750
- Denominator = sqrt(250 * 750) = sqrt(187500) = 433.01
- r = 500 / 433.01 = 1.1547... (check your sums!)