Pearson Correlation Calculator

Pearson Correlation is evaluated from X Values and Y Values. The calculation reports Pearson r, R^2 and Correlation Strength.

Results

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About the Pearson Correlation Calculator

Pearson Correlation is treated here as a quantitative relation between X Values and Y Values and Pearson r, R^2, Correlation Strength and Number of Data Pairs.

The calculator uses a multi formula configuration. Each reported value is read as a direct evaluation of the stored rules with the declared field formats and units.

Formula basis:
r = Sigma(xᵢ - x̄)(yᵢ - ȳ) / sqrt[Sigma(xᵢ - x̄)^2 x Sigma(yᵢ - ȳ)^2]
R^2 = r^2 (proportion of variance explained)

Interpret the outputs in the order shown by the result fields. Optional inputs affect only the outputs that depend on those variables.

Formula & How It Works

The calculation applies the following relations exactly as recorded in the metadata:

r = Sigma(xᵢ - x̄)(yᵢ - ȳ) / sqrt[Sigma(xᵢ - x̄)^2 x Sigma(yᵢ - ȳ)^2]
R^2 = r^2 (proportion of variance explained)

Each output field is produced by substituting the supplied inputs into the relevant relation and then applying the declared rounding or text format.

Worked Examples

Example 1: Height vs. Weight

Inputs

x_data: 62, 64, 66, 68, 70, 72, 74 y_data: 115, 130, 145, 160, 175, 185, 200
Pearson r: 0.9988. R^2: 0.997602. Correlation Strength: Very Strong. Number of Data Pairs: 7

With X Values = 62, 64, 66, 68, 70, 72, 74 and Y Values = 115, 130, 145, 160, 175, 185, 200 as the stated inputs, the result is Pearson r = 0.9988, R^2 = 0.997602 and Correlation Strength = Very Strong. Each value corresponds to the declared output fields.

Example 2: Study Hours vs. GPA

Inputs

x_data: 1, 2, 3, 4, 5, 6, 7, 8 y_data: 1.8, 2.1, 2.5, 2.7, 3.0, 3.3, 3.5, 3.8
Pearson r: 0.997711. R^2: 0.995428. Correlation Strength: Very Strong. Number of Data Pairs: 8

With X Values = 1, 2, 3, 4, 5, 6, 7, 8 and Y Values = 1.8, 2.1, 2.5, 2.7, 3.0, 3.3, 3.5, 3.8 as the stated inputs, the result is Pearson r = 0.997711, R^2 = 0.995428 and Correlation Strength = Very Strong. Each value corresponds to the declared output fields.

Example 3: Temperature vs. Heating Cost

Inputs

x_data: 25, 30, 35, 40, 45, 50, 55, 60 y_data: 380, 320, 270, 225, 180, 140, 100, 60
Pearson r: -0.99767. R^2: 0.995345. Correlation Strength: Very Strong. Number of Data Pairs: 8

With X Values = 25, 30, 35, 40, 45, 50, 55, 60 and Y Values = 380, 320, 270, 225, 180, 140, 100, 60 as the stated inputs, the result is Pearson r = -0.99767, R^2 = 0.995345 and Correlation Strength = Very Strong. Each value corresponds to the declared output fields.

Example 4: Advertising Spend vs. Sales

Inputs

x_data: 1000, 2000, 2500, 3000, 4000, 5000, 6000 y_data: 9500, 11000, 12500, 12000, 14500, 15000, 14800
Pearson r: 0.939747. R^2: 0.883124. Correlation Strength: Very Strong. Number of Data Pairs: 7

With X Values = 1000, 2000, 2500, 3000, 4000, 5000, 6000 and Y Values = 9500, 11000, 12500, 12000, 14500, 15000, 14800 as the stated inputs, the result is Pearson r = 0.939747, R^2 = 0.883124 and Correlation Strength = Very Strong. Each value corresponds to the declared output fields.

Common Use Cases

  • Measure relationship between height and weight
  • Correlate advertising spend with sales
  • Assess strength of predictive relationships
  • Check assumptions for linear regression