Math & Statistics
Correlation Calculator
Calculate Pearson correlation for three entered coordinate pairs and show the associated least-squares slope, intercept, and fitted y value at the third entered x. The page separates standardized association from the unit-dependent fitted line.
Pearson correlation-
Associated regression slope-
Associated intercept-
Predicted Y at entered X3-
Decision view
Coordinate-pair relationship and fitted direction
Coordinate-pair relationship and fitted directionThe entered pairs remain visible as individual observations while the fitted line and Pearson coefficient summarize their linear direction.
Exact scenario comparisonX3 changes while all other entered assumptions remain constant.
| X3 | Pearson correlation | Associated regression slope | Associated intercept | Predicted Y at entered X3 |
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How to use Correlation Calculator
- Enter three correctly paired observations; each x value and y value on the same numbered row must describe the same case.
- Interpret the sign as direction and the magnitude as linear alignment, while inspecting whether one point or a nonlinear pattern drives the value.
- Use the displayed slope and fitted value only as a description of this three-point line, not as evidence of a causal effect or reliable forecast.
Calculator guide
Understanding Correlation Calculator
Pearson correlation measures the direction and strength of a linear relationship after both variables are centered and scaled. It is unit-free, but it is not resistant to influential points and does not establish that changing x will cause y to change.
Calculation method
How the calculation works
Standardize the covariance of three coordinate pairs by their variation to estimate Pearson correlation and the associated fitted line. Standardize the covariance of three coordinate pairs by their variation to estimate Pearson correlation and the associated fitted line.
Interpretation matrix
Ask four questions before reporting correlation
A coefficient needs graphical, measurement, and design context.
Report the coordinate plot and observation count with the coefficient whenever possible.
Worked situations
Practical examples
- For (10,18), (15,26), and (22,35), both variables rise together, producing a strong positive correlation.
- Multiplying every y value by 100 changes slope and intercept but leaves Pearson correlation unchanged because correlation is standardized.
- Reversing the order of y while keeping x increasing can create a negative correlation, indicating opposite linear direction rather than negative y values.
Better inputs
Useful tips
- Plot the coordinate pairs; the same correlation can arise from different slopes, scales, clusters, and outlier patterns.
- Do not correlate totals or cumulative time series without checking shared trends and dependence.
- Use more observations and prespecified analysis rules for any inferential, scientific, or operational conclusion.
Before relying on the result
Limitations and common mistakes
- Three pairs provide only a minimal illustration and make the coefficient extremely sensitive to each observation.
- Pearson correlation summarizes linear association and can be near zero despite a strong curved relationship.
- The page does not provide confidence intervals, significance tests, rank correlation, missing-data handling, weights, or repeated-measures adjustment.
Reference
Key terms
- Pearson correlation
- Standardized covariance ranging from -1 to 1 when both variables have nonzero variation.
- Positive association
- Larger x values tend to occur with larger y values in a linear pattern.
- Negative association
- Larger x values tend to occur with smaller y values in a linear pattern.
- Paired observation
- An x and y measurement belonging to the same case, time, or experimental unit.
Important note
Calculated directly from the entered values using the displayed formula and rounding settings.
Frequently asked questions
Can correlation exceed 1?
No. A valid Pearson correlation lies between -1 and 1; undefined cases occur when either variable has zero variation.
Does zero correlation mean no relationship?
No. It means no linear association in the entered data; a nonlinear relationship may still be present.
Why is the fitted value at X3 not always equal to Y3?
The regression line minimizes squared residuals across all three pairs and does not generally pass through every observation.
Is a strong correlation statistically significant?
Not necessarily. Significance depends on sample size, assumptions, study design, and the analysis plan; this page does not perform that test.