Measure paired relationships with reliable statistical output. See direction, strength, and practical interpretation in seconds. Export clean results, summary tables, and reports for review.
| Pair | X | Y |
|---|---|---|
| 1 | 2 | 3 |
| 2 | 4 | 5 |
| 3 | 6 | 7 |
| 4 | 8 | 9 |
| 5 | 10 | 11 |
| 6 | 12 | 14 |
Use this dataset to test the calculator quickly and review a strong positive linear relationship.
Pearson r-factor formula:
r = [nΣxy − (Σx)(Σy)] / √{[nΣx² − (Σx)²][nΣy² − (Σy)²]}
Coefficient of determination: r²
Sample covariance: Σ[(x − x̄)(y − ȳ)] / (n − 1)
Regression line: y = a + bx
Slope: b = [nΣxy − (Σx)(Σy)] / [nΣx² − (Σx)²]
Intercept: a = ȳ − bx̄
The calculator also reports a t statistic to help you inspect the strength of linear association for the entered sample.
An r-factor calculator measures the linear relationship between two numeric variables. It helps you see whether values move together, move apart, or show little pattern. In maths, this value is often called Pearson’s correlation coefficient. It ranges from -1 to 1. A result near 1 shows a strong positive relationship. A result near -1 shows a strong negative relationship. A result near 0 shows weak linear association.
This calculator accepts paired x and y values. It then computes the r-factor, coefficient of determination, covariance, means, and a simple regression line. You also get a strength label for faster interpretation. That saves time during homework, research, quality checks, and data review.
The r-factor is useful because it turns a scattered dataset into one clear summary. It helps students compare variables with confidence. It also supports teachers, analysts, and researchers who need a quick relationship check. A positive value means both variables tend to rise together. A negative value means one variable often falls when the other rises.
Still, correlation does not prove causation. Two variables can move together for many reasons. Always review the context, the sample size, and the scatter pattern. A high r-factor can still hide outliers or non linear structure. That is why this page also reports supporting statistics.
Use the absolute value of r to judge strength. Very small values suggest little practical relationship. Mid range values suggest moderate association. Large values suggest a strong linear trend. The r squared value explains how much variance in y is linked to x through the fitted line. The slope and intercept help you build a simple prediction equation.
Use this calculator for classroom datasets, lab results, business metrics, and paired observations from surveys. You can paste values quickly, test examples, export the summary, and keep a clean record. The layout stays simple, so the focus remains on the maths and the result.
For best results, use matched pairs only. Remove text labels and blank entries. Check units before calculation carefully. Consistent units improve interpretation and reduce confusion when you compare several datasets over time.
Here, the r-factor means Pearson correlation coefficient. It measures the linear relationship between paired X and Y values. It ranges from -1 to 1.
There is no universal cutoff. Values closer to 1 or -1 usually show stronger linear relationships. Values near 0 usually show weak linear association.
No. Correlation only shows how two variables move together. It does not prove that one variable causes the other.
Each X value must match one Y value. The formula uses paired observations. Unequal lengths break that pairing and make the result invalid.
r² shows the proportion of variation in Y linked to X through the fitted linear model. It is often called explained variance.
The r-factor becomes undefined. Correlation needs variation in both variables. If all X values or all Y values are the same, the denominator becomes zero.
Yes. The calculator accepts integers, decimals, and negative numbers. Just keep the values numeric and properly paired.
The optional prediction X field uses the fitted regression line. It estimates a Y value from the slope and intercept.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.