Turn raw numbers into standardized insights and predictions. Built for students, analysts, and researchers everywhere. Enter data, press calculate, then export your report easily.
You can load this dataset into the calculator using the “Load example” button.
| # | x | y |
|---|---|---|
| 1 | 10 | 12 |
| 2 | 11 | 14 |
| 3 | 12 | 15 |
| 4 | 13 | 16 |
| 5 | 14 | 18 |
| 6 | 15 | 19 |
| 7 | 16 | 21 |
| 8 | 17 | 22 |
This calculator combines z-scores with simple linear regression to standardize the relationship between two variables. Standardization converts raw values into standard deviation units, making results comparable across different measurement scales. The standardized prediction uses correlation to estimate the expected standardized outcome for a given input.
A one-unit change in z_x equals a one standard deviation shift in X. The calculator converts that shift into z_y_hat and then back into original Y units for an interpretable prediction.
Dataset mode accepts paired observations typed line by line using commas, tabs, semicolons, or spaces. It computes μx, μy, sample σx, sample σy, and Pearson’s r from your pairs. Summary mode is useful when μ, σ, and r are already known from a report.
To protect accuracy, the calculator ignores incomplete rows, blocks non-numeric values, and prevents division by zero. If σx or σy equals zero, standardization cannot proceed because variability is required.
Outputs include μ and σ for both variables, correlation r, and two equivalent regression forms. Standardized form is z_y_hat = r·z_x. Unstandardized form is y_hat = b0 + b1·x, where b1 = r(σy/σx) and b0 = μy − b1μx.
Dataset mode also provides z_x, z_y, fitted ŷ, fitted z_y_hat, and residuals per row for checking and troubleshooting.
Correlation r summarizes direction and strength. Values near 0 imply weak linear association, while values closer to ±1 imply stronger linear association. For instance, r = 0.80 indicates a strong positive relationship, and r = −0.30 indicates a modest negative relationship.
Standardized prediction z_y_hat expresses the expected change in Y in standard deviation units. Residuals (y − ŷ) show where observations sit above or below the fitted line and can flag outliers or curvature.
CSV export includes summary values and row-level calculations for reconciliation in spreadsheets. PDF export produces a compact report for sharing, including the method and coefficients.
Together, exports support QA checks, reproducible results, and clear documentation of inputs and predictions. Use the downloads to archive calculations alongside datasets, notes, and assumptions securely later.
A z-score shows how far a value is from its mean in standard deviation units. Positive values are above the mean, negative values are below it, and zero equals the mean.
When both variables are standardized, the regression intercept becomes zero and the slope equals Pearson’s r. This is why the calculator uses zŷ = r·zx for standardized predictions.
Dataset mode uses the sample standard deviation, dividing by (n−1). This matches common statistical practice for estimating variability from observed samples rather than assuming a full population.
Yes. Summary mode lets you predict using μx, σx, μy, σy, and r. Enter either a raw x value or a z-score for x, and the calculator returns zŷ and ŷ.
If all X values or all Y values are identical, there is no variation to standardize or model. Add more diverse observations, or verify that your data is not duplicated or rounded excessively.
Residuals are the differences between observed y and predicted ŷ. Large residuals can signal unusual points, measurement issues, or a relationship that is not well captured by a straight line.
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.