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  3. /Statistics for Biology
  4. /Correlation Coefficient Calculator

Correlation Coefficient Calculator

Last updated: February 24, 2026

Calculator

Results

Correlation Coefficient

0.680336

Coefficient of Determination

0.462857

Covariance Numerator

90

X Variation Term

50

Y Variation Term

350

Correlation Denominator

132.287566

Results

Correlation Coefficient

0.680336

Coefficient of Determination

0.462857

Covariance Numerator

90

X Variation Term

50

Y Variation Term

350

Correlation Denominator

132.287566

The Correlation Coefficient Calculator computes Pearson's r and R squared from summary statistics. It measures the strength and direction of the linear relationship between two variables in biological research.

Visual Analysis

How It Works

r = (nΣxy - ΣxΣy) / √[(nΣx² - (Σx)²)(nΣy² - (Σy)²)]

Values range from -1 (perfect negative) through 0 (no correlation) to +1 (perfect positive). R² indicates the proportion of variance explained.

Worked Examples

Strong Positive Correlation

Inputs

n5
sum x15
sum y40
sum xy138
sum x255
sum y2390

Results

r0.9
r squared0.81

r = 0.9 indicates a strong positive linear relationship.

Weak Correlation

Inputs

n6
sum x21
sum y22
sum xy78
sum x291
sum y2100

Results

r0.12
r squared0.014

r = 0.12 shows very weak positive correlation.

Frequently Asked Questions

No. Correlation measures association, not causation. Establishing causation requires controlled experiments.

|r| of 0.9-1.0 is very strong, 0.7-0.9 strong, 0.5-0.7 moderate, 0.3-0.5 weak, below 0.3 negligible.

Both variables are continuous, the relationship is linear, data are approximately normally distributed, and no significant outliers.

Sources & Methodology

Zar, J.H. Biostatistical Analysis. Sokal, R.R. & Rohlf, F.J. Biometry.
R

Roboculator Team

The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.

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