Correlation Coefficient Calculator

This calculator helps finance professionals and statisticians to determine the correlation coefficient between two data sets. It aids in understanding how two variables are linearly related, which is crucial for risk management and portfolio diversification.

Calculate Correlation Coefficient

Results

Correlation Coefficient N/A

Data Source and Methodology

All calculations are based strictly on the formulas and data provided by the authoritative data source. For more details, please refer to the original source document available here.

The Formula Explained

\( r = \frac{n(\sum xy) - (\sum x)(\sum y)}{\sqrt{[n\sum x^2 - (\sum x)^2][n\sum y^2 - (\sum y)^2]}} \)

Glossary of Variables

  • Data Set X: The first set of numerical data.
  • Data Set Y: The second set of numerical data.
  • Correlation Coefficient (r): A measure of the strength and direction of a linear relationship between two variables.

How It Works: A Step-by-Step Example

Consider data sets X = [1, 2, 3] and Y = [4, 5, 6]. The steps to calculate the correlation coefficient are as follows:

  1. Calculate the sums of each data set and their squares.
  2. Compute the sum of the products of paired scores.
  3. Insert these values into the correlation coefficient formula.
  4. Interpret the resulting coefficient.

Frequently Asked Questions (FAQ)

What is a correlation coefficient?

A correlation coefficient is a statistical measure of the degree to which changes to the value of one variable predict change to the value of another.

How do I calculate a correlation coefficient?

The correlation coefficient can be calculated using the formula: \( r = \frac{n(\sum xy) - (\sum x)(\sum y)}{\sqrt{[n\sum x^2 - (\sum x)^2][n\sum y^2 - (\sum y)^2]}} \)

Why is the correlation coefficient important in finance?

In finance, the correlation coefficient is used to measure the relationship between two securities' returns, helping to create diversified portfolios.

What do the values of the correlation coefficient mean?

A value of 1 implies a perfect positive linear relationship, -1 implies a perfect negative linear relationship, and 0 implies no linear relationship.

Tool developed by Ugo Candido. Content verified by the CalcDomain Expert Team. Last reviewed for accuracy on: September 15, 2024.