Correlation Coefficient Calculator - Mathematical Calculations & Solutions

Separate values with commas

Must match number of X values

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How It Works

1

Input Data Pairs

Enter X and Y values separated by commas

2

Calculate Pearson r

Apply statistical correlation formula

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Analyze relationship strength

Common Examples

Height vs Weight: r = +0.85
Strong positive correlation
Temperature vs Heating Cost: r = -0.92
Very strong negative correlation
Study Hours vs Test Score: r = +0.78
Strong positive correlation
Shoe Size vs IQ: r = 0.02
No correlation (random)
Pearson Correlation Formula
r = Σ[(xi - x̄)(yi - ȳ)] / √[Σ(xi - x̄)²Σ(yi - ȳ)²]
Where: xi, yi are data points; x̄, ȳ are means
Range: -1 ≤ r ≤ +1
Interpretation: Closer to ±1 = stronger linear relationship

Correlation Coefficient Calculator

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What

Measure the strength and direction of linear relationships between two variables.

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Why

Essential for data analysis, research, statistics, and understanding variable relationships.

Applications

Statistics, research, finance, psychology, economics, and scientific studies.

Calculation Table

Correlation RangeStrengthExampleInterpretation
±0.90 to ±1.00Very Strongr = +0.95Almost perfect linear relationship
±0.70 to ±0.89Strongr = -0.82Strong linear relationship
±0.50 to ±0.69Moderater = +0.65Moderate linear relationship
±0.30 to ±0.49Weakr = -0.35Weak linear relationship
0.00 to ±0.29Very Weakr = 0.15Little to no linear relationship

Frequently Asked Questions

1

What is a correlation coefficient?

A correlation coefficient (r) measures the strength and direction of a linear relationship between two variables, ranging from -1 to +1.

2

How do I input my data?

Enter X values in the first box and Y values in the second box, separated by commas. Both datasets must have the same number of values.

3

What does r = 0.8 mean?

An r value of 0.8 indicates a strong positive correlation, meaning as one variable increases, the other tends to increase proportionally.

4

What's the difference between positive and negative correlation?

Positive correlation: both variables move in the same direction. Negative correlation: variables move in opposite directions.

5

Does correlation prove causation?

No! Correlation only shows association. High correlation doesn't mean one variable causes changes in the other - there could be other factors involved.

6

What if my correlation is close to zero?

A correlation near zero (e.g., -0.1 to +0.1) suggests little to no linear relationship between the variables, though non-linear relationships may still exist.

7

Can I use this for any type of data?

This calculator works best with continuous numerical data. For categorical or ordinal data, other correlation methods like Spearman's rank correlation may be more appropriate.

Quick Reference

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