Turn historical pairs into forecast-ready regression insights. Compare linear, polynomial, and transformed models. Export results as CSV or printable reports today.
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| x | y |
|---|---|
| 1 | 12 |
| 2 | 15 |
| 3 | 18 |
| 4 | 22 |
| 5 | 27 |
| 6 | 30 |
| 7 | 34 |
| 8 | 37 |
| 9 | 41 |
| 10 | 45 |
Use at least 10 paired rows for dependable error metrics and model comparison. Two points can fit a line, but the results are fragile and may not generalize beyond the observed range.
These models use logarithms during fitting. Exponential needs positive y values, and power needs positive x and y values. Remove zeros, correct units, or choose linear/polynomial when positivity cannot be guaranteed.
Not always. A slightly higher R² may come from overfitting, especially with polynomials. Compare RMSE/MAE, check residual patterns, and sanity-check forecasts outside the sample range before deciding.
It is an approximate uncertainty band computed as prediction ± z·sigma, where sigma is residual spread. It assumes roughly normal errors and constant variance, so it is best treated as a quick guide.
Yes. Enter multiple x values separated by commas, spaces, or semicolons. The calculator outputs a forecast row for each x, and exports the same list in both CSV and PDF reports.
Replot x versus y and y-hat, review residuals, and confirm the equation matches expectations. Keep the exported metrics with the original dataset, so later updates can be compared consistently.
Effective regression forecasts start with clean, paired observations where each x maps to one y. Remove duplicates caused by repeated logging, ensure consistent units, and keep the x scale meaningful (time index, spend level, temperature, or volume). Standardize time gaps, because uneven spacing can bias trend interpretation and forecast timing. A simple range check helps: extreme outliers can dominate least squares and distort coefficients. When you paste data, aim for at least 10 rows so error metrics stabilize and comparisons across models become clearer.
Linear fits are best when changes in y per unit x stay roughly constant. Polynomial degree 2 or 3 captures curvature but can overfit if the dataset is short or noisy; watch for unrealistic swings outside the observed x range. Exponential growth assumes proportional change, while the power model assumes scale effects that grow or shrink with x. Use transformed models only when y (and x for power) stays positive.
R and R² summarize association and explained variance, but they do not guarantee useful forecasts. RMSE and MAE are scale based and compare average error magnitudes; RMSE penalizes large misses more strongly. MAPE expresses error as a percentage, yet it becomes unstable when actual values are near zero. SSE supports comparing variants on the same dataset and is the base for residual spread estimation.
After fitting, enter one or many forecast x values to generate predicted y. The optional interval uses residual sigma with a normal approximation, giving a quick “typical” uncertainty band around predictions. Wider bands indicate noisier data or weaker fit. Intervals are not a guarantee; structural breaks, seasonality, or missing drivers can widen real uncertainty beyond the displayed bounds.
CSV export captures the chosen equation, metrics, historical fitted values, and forecast rows, making it easy to replot or audit in spreadsheets. PDF export provides a compact report for stakeholders and documentation. For best practice, save the raw dataset alongside the export, note the model choice rationale, and rerun the fit when new observations materially change the trend.
Use at least 10 paired rows for dependable error metrics and model comparison. Two points can fit a line, but the results are fragile and may not generalize beyond the observed range.
These models use logarithms during fitting. Exponential needs positive y values, and power needs positive x and y values. Remove zeros, correct units, or choose linear/polynomial when positivity cannot be guaranteed.
Not always. A slightly higher R² may come from overfitting, especially with polynomials. Compare RMSE/MAE, check residual patterns, and sanity-check forecasts outside the sample range before deciding.
It is an approximate uncertainty band computed as prediction ± z·sigma, where sigma is residual spread. It assumes roughly normal errors and constant variance, so it is best treated as a quick guide.
Yes. Enter multiple x values separated by commas, spaces, or semicolons. The calculator outputs a forecast row for each x, and exports the same list in both CSV and PDF reports.
Replot x versus y and y-hat, review residuals, and confirm the equation matches expectations. Keep the exported metrics with the original dataset, so later updates can be compared consistently.
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.