Key Facts
- Category
- Math, Date & Finance
- Input Types
- textarea, text, number, checkbox
- Output Type
- json
- Sample Coverage
- 3
- API Ready
- Yes
Overview
The Pearson Correlation Calculator is a statistical utility designed to measure the linear association between two numeric variables. By inputting paired data, you can instantly determine the Pearson correlation coefficient (r), R-squared value, covariance, and Fisher confidence intervals, making it easy to evaluate the strength and direction of linear relationships.
When to Use
- •When you need to measure the strength and direction of a linear relationship between two continuous numeric variables.
- •When evaluating the predictive power of a linear regression model using the R-squared value.
- •When determining if two sets of numeric data move together, such as comparing study hours to test scores or marketing spend to revenue.
How It Works
- •Enter your paired numeric data into the main text area, with one pair per line separated by a comma.
- •Alternatively, paste your X and Y values into their respective separate input fields as comma-separated lists.
- •Adjust the decimal places, confidence level, and toggle the regression line calculation as needed.
- •The tool processes the data and outputs a JSON result containing the Pearson r, R-squared, covariance, and regression formula.
Use Cases
Examples
1. Analyzing Study Time vs. Test Scores
Educator- Background
- A teacher wants to understand how the number of hours students study impacts their final exam scores.
- Problem
- Needs to calculate the linear correlation and regression line to predict future scores based on study habits.
- How to Use
- Paste the paired data (hours, score) into the Data Pairs field and ensure 'Include Regression Line' is checked.
- Example Config
-
{ "pairedData": "1, 52\n2, 57\n3, 63\n4, 68\n5, 74", "includeRegressionLine": true } - Outcome
- The tool outputs a Pearson r of 0.9995 and an R-squared of 0.999, indicating a near-perfect positive linear relationship, along with the regression equation.
2. Evaluating Marketing Spend vs. Revenue
Marketing Analyst- Background
- An analyst has monthly data for advertising spend and the resulting sales revenue.
- Problem
- Needs to determine the R-squared value to see how much of the revenue variance is explained by ad spend.
- How to Use
- Input the ad spend in the X Values field and revenue in the Y Values field, setting the confidence level to 95%.
- Example Config
-
{ "xValues": "1000, 1500, 2000, 2500", "yValues": "5000, 6200, 7100, 8500", "confidenceLevel": 95 } - Outcome
- Calculates the Pearson correlation and R-squared, providing statistical evidence of the marketing campaign's effectiveness and a 95% confidence interval for the correlation.
Try with Samples
math-&-numbersFAQ
What does a Pearson r value of 1 or -1 mean?
A value of 1 indicates a perfect positive linear relationship, while -1 indicates a perfect negative linear relationship. A value of 0 means there is no linear correlation.
What is the difference between Pearson r and R-squared?
Pearson r measures the strength and direction of the linear relationship. R-squared represents the proportion of variance in the dependent variable that can be explained by the independent variable.
Can I input X and Y values separately?
Yes, you can either paste paired data (X, Y) on each line in the primary input or use the dedicated X Values and Y Values fields for comma-separated lists.
What is the Fisher confidence interval?
It is a statistical range that estimates the true population correlation coefficient based on your sample data and selected confidence level (e.g., 95%).
Does this tool calculate the regression line?
Yes, if the 'Include Regression Line' option is checked, the tool calculates the least-squares regression line equation alongside the correlation metrics.