Build precise trend models from pasted x and y values. Inspect diagnostics before exporting results. Make faster math decisions with transparent regression summaries today.
Use this sample to test the calculator quickly.
| X | Y |
|---|---|
| 1 | 1.8 |
| 2 | 2.6 |
| 3 | 3.7 |
| 4 | 4.1 |
| 5 | 5.0 |
| 6 | 6.2 |
| 7 | 6.8 |
| 8 | 8.1 |
| 9 | 8.9 |
| 10 | 10.2 |
The calculator fits the line ŷ = a + bx.
b = Σ[(xᵢ − x̄)(yᵢ − ȳ)] / Σ[(xᵢ − x̄)²]
a = ȳ − b x̄
Residual = yᵢ − ŷᵢ
R² = 1 − (SSE / SST)
RMSE = √(SSE / df_error)
When zero-intercept mode is enabled, the slope becomes b = Σ(xᵢyᵢ) / Σ(xᵢ²) and the intercept is fixed at 0.
Reliable regression starts with clean paired values in two columns, one predictor and one response. The calculator accepts comma, tab, semicolon, or space separators, plus an optional header row. For diagnostics, keep units consistent and avoid mixed scales. The included example has 10 observations from X=1 to X=10. This structure supports stable estimates, review, and fast exports for daily reporting workflows. Clear formatting reduces entry errors and speeds validation before model interpretation.
With the example data, the fitted line is approximately y-hat = 0.7067 + 0.9152x. The slope shows average response change per one-unit increase in X, while the intercept estimates baseline response at X=0. The coefficient output reports standard errors and t statistics, helping users judge estimate stability. In this sample, the slope is positive, confirming a consistent upward relationship across the observed range. Coefficients support forecasting and benchmarking when assumptions remain reasonable.
Residual analysis explains how far observations fall from the fitted line. In the sample, SSE is about 0.4701 and RMSE is about 0.2424, indicating small average prediction error relative to the Y scale. The residual table lists actual values, predicted values, and row-level differences, which supports quick outlier checks. Users should look for random residual spread instead of patterns, because trends can signal nonlinearity or missing variables in practice. Review unusual rows before sharing conclusions.
Model strength is summarized by correlation and explained variance. The example produces r near 0.9966 and R-squared near 0.9932, meaning the line explains most observed variation in Y. The ANOVA block separates regression and error sums of squares, then reports an F statistic near 1175.92. High explained variation does not prove causation, but it provides strong evidence that the predictor is useful. Apply domain knowledge before final recommendations carefully.
This calculator is designed for repeatable analytical work. Teams can paste fresh paired data, choose decimal precision, and optionally generate a prediction for a target X value. Results appear above the form for immediate validation before export. CSV output preserves model summary, coefficients, ANOVA, predictions, and residual rows for audits. PDF output captures a compact report suitable for project files, stakeholder reviews, and documented decision support. Consistent exports improve collaboration and traceability.
Paste two numeric columns representing X and Y pairs. Use comma, tab, semicolon, or spaces as separators. You may keep a header row if the header checkbox is enabled before calculation.
Use zero-intercept mode only when your process must pass through the origin and that assumption is justified. Otherwise, let the calculator estimate the intercept from the observed data.
R squared shows the share of Y variation explained by the fitted line. Values closer to 1 indicate stronger linear fit, but they do not prove causation or guarantee future performance.
Residuals reveal model error for each row. Large or patterned residuals can indicate outliers, data entry mistakes, nonlinear behavior, or missing predictors that simple linear regression cannot capture.
This version provides coefficient estimates, standard errors, t statistics, ANOVA, and fit metrics. It does not currently display p-values or confidence intervals, so use external statistical tools if required.
CSV export includes model summary, coefficients, ANOVA, prediction output, and residual rows. PDF export provides a compact report summary for sharing, filing, and quick stakeholder review.
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.