Correlation Coefficient Calculator
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Correlation Coefficient Calculator
Data Set X (comma-separated values):
Data Set Y (comma-separated values):
Calculate Correlation
Reset
Correlation Coefficient (r)
—
Understanding the Correlation Coefficient
The correlation coefficient, often denoted by 'r', is a statistical measure that describes the strength and direction of a linear relationship between two variables. It ranges from -1 to +1.
+1: Perfect positive linear correlation. As one variable increases, the other increases proportionally.-1: Perfect negative linear correlation. As one variable increases, the other decreases proportionally.0: No linear correlation. There is no discernible linear relationship between the two variables.Values between 0 and +1 indicate a positive correlation of varying strength.
Values between 0 and -1 indicate a negative correlation of varying strength.
A correlation coefficient close to +1 or -1 suggests a strong linear relationship, while a value close to 0 suggests a weak or non-existent linear relationship. It's crucial to remember that correlation does not imply causation; a strong correlation between two variables doesn't necessarily mean one causes the other.
How it's Calculated (Pearson's r)
This calculator uses Pearson's correlation coefficient, which is calculated using the following formula:
r = Σ[(xi - x̄)(yi - ȳ)] / √[Σ(xi - x̄)² * Σ(yi - ȳ)²]
Where:
xi and yi are the individual data points for variable X and variable Y, respectively.x̄ and ȳ are the means (averages) of variable X and variable Y, respectively.Σ denotes summation.
In simpler terms, the formula calculates the covariance of the two variables and normalizes it by the product of their standard deviations.
Use Cases
The correlation coefficient is widely used in various fields:
Finance: To understand the relationship between stock prices, market indices, or economic indicators.Economics: To analyze relationships between economic variables like inflation and unemployment.Science: To study relationships between experimental measurements, such as temperature and reaction rates.Social Sciences: To examine relationships between survey responses or demographic data.Machine Learning: To identify feature dependencies and multicollinearity.
function calculateCorrelation() {
var dataXInput = document.getElementById("dataX").value;
var dataYInput = document.getElementById("dataY").value;
var dataX = dataXInput.split(',').map(function(item) { return parseFloat(item.trim()); });
var dataY = dataYInput.split(',').map(function(item) { return parseFloat(item.trim()); });
// Validate input
if (dataX.some(isNaN) || dataY.some(isNaN)) {
document.getElementById("correlationResult").innerText = "Invalid input. Please enter numbers only.";
return;
}
if (dataX.length !== dataY.length) {
document.getElementById("correlationResult").innerText = "Data sets must have the same number of points.";
return;
}
if (dataX.length < 2) {
document.getElementById("correlationResult").innerText = "At least two data points are required.";
return;
}
var n = dataX.length;
var sumX = 0;
var sumY = 0;
var sumXY = 0;
var sumX2 = 0;
var sumY2 = 0;
for (var i = 0; i < n; i++) {
sumX += dataX[i];
sumY += dataY[i];
sumXY += dataX[i] * dataY[i];
sumX2 += dataX[i] * dataX[i];
sumY2 += dataY[i] * dataY[i];
}
var numerator = n * sumXY – sumX * sumY;
var denominator = Math.sqrt((n * sumX2 – sumX * sumX) * (n * sumY2 – sumY * sumY));
if (denominator === 0) {
document.getElementById("correlationResult").innerText = "Cannot calculate (division by zero). Data might be constant.";
return;
}
var correlation = numerator / denominator;
// Display result
document.getElementById("correlationResult").innerText = correlation.toFixed(4);
}
function resetForm() {
document.getElementById("dataX").value = "";
document.getElementById("dataY").value = "";
document.getElementById("correlationResult").innerText = "–";
}