Correlation Coefficient Calculator

Calculate the Pearson correlation coefficient (r) between two variables from summary statistics.

Pearson r

1.154701

R-squared1.333333
Numeratore500.0000
Denominatore433.0127

Pearson r vs Number of Pairs (n)

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Formula

## 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.

Esempio Risolto

5 data pairs with given sums: Sum(xy)=2350, Sum(x)=75, Sum(y)=150, Sum(x^2)=1175, Sum(y^2)=4650.

  1. 01Numerator = 5*2350 - 75*150 = 11750 - 11250 = 500
  2. 02Denom part 1 = 5*1175 - 75^2 = 5875 - 5625 = 250
  3. 03Denom part 2 = 5*4650 - 150^2 = 23250 - 22500 = 750
  4. 04Denominator = sqrt(250 * 750) = sqrt(187500) = 433.01
  5. 05r = 500 / 433.01 = 1.1547... (check your sums!)