Pearson Correlation Coefficient Calculator for Moderate Negative Correlation
Example of a moderate negative relationship with a correlation coefficient around -0.5.
Calculates the Pearson correlation coefficient using covariance and standard deviations of two variables. Enter your Covariance of X and Y, Standard Deviation of X, Standard Deviation of Y to get an instant pearson correlation coefficient. Formula: covariance / (std_dev_x * std_dev_y).
Pearson Correlation Coefficient
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How It Works
How It Works
This calculator finds the Pearson correlation coefficient, which measures how strongly two variables move together. It uses the covariance between the variables and divides it by the product of their standard deviations.
The formula is: covariance / (std_dev_x * std_dev_y). The result is always a single number that shows the direction and strength of the relationship between the two variables.
- Enter the covariance of X and Y
- Enter the standard deviation of X
- Enter the standard deviation of Y
- The calculator divides covariance by both standard deviations multiplied together
- The result is a unitless correlation coefficient
Understanding the Results
The Pearson correlation coefficient ranges from -1 to 1. A value near 1 means the variables increase together, while a value near -1 means one variable decreases as the other increases.
A value close to 0 suggests little or no linear relationship between the variables. The closer the value is to either extreme, the stronger the relationship.
- 1 indicates a strong positive relationship
- -1 indicates a strong negative relationship
- 0 indicates little or no linear relationship
- Values closer to 1 or -1 show stronger relationships
- The result has no physical unit
Frequently Asked Questions
What does the Pearson Correlation Coefficient Calculator measure?
This calculator measures the strength and direction of the linear relationship between two variables. It uses the covariance of the variables along with their standard deviations to calculate the Pearson correlation coefficient. The result is a unitless value between -1 and 1.
How is the Pearson correlation coefficient calculated?
The calculator uses the formula: covariance divided by the product of the standard deviation of X and the standard deviation of Y. In mathematical form, it is covariance / (std_dev_x × std_dev_y). This standardizes the covariance so the result can be easily interpreted.
What do positive, negative, and zero correlation values mean?
A positive correlation means the two variables tend to increase together, while a negative correlation means one variable tends to decrease when the other increases. A value close to 0 suggests little or no linear relationship. Values closer to 1 or -1 indicate stronger relationships.
When should I use this calculator?
Use this calculator when you already know the covariance and standard deviations of two variables and want to quickly determine their Pearson correlation coefficient. It is commonly used in statistics, finance, economics, psychology, and data analysis. For example, it can measure how closely stock returns move together.
Why must the standard deviations be nonzero?
The formula divides by the product of the standard deviations, so both values must be greater than zero. If either standard deviation is zero, the calculation becomes undefined because one of the variables has no variation. Enter valid positive standard deviation values for accurate results.
Does the calculator return a unit or percentage?
No, the Pearson correlation coefficient is unitless because the standardization process removes measurement units. The output is a pure numeric value that indicates relationship strength and direction. For example, a result of 0.85 indicates a strong positive linear correlation.
Disclaimer
This calculator provides estimates for informational purposes only. It is not professional advice. Verify results with a qualified professional. Disclaimer.