Model time‑indexed values with trend and lags fast. Add seasonality dummies for clearer forecasts now. Download tables, metrics, and charts for confident decisions everywhere.
Paste two columns: period label and value. Choose options, then calculate. Results appear above this form after you submit.
This small sample shows an upward trend with mild variation.
| Period | Value |
|---|---|
| 2025-01 | 120 |
| 2025-02 | 128 |
| 2025-03 | 133 |
| 2025-04 | 142 |
| 2025-05 | 151 |
| 2025-06 | 149 |
| 2025-07 | 160 |
| 2025-08 | 168 |
This calculator fits an ordinary least squares model with optional terms:
Coefficients are estimated by: β̂ = (XᵀX)⁻¹ Xᵀ y.
Error metrics include RMSE, MAE, and MAPE, plus R² when variance exists.
Time series regression turns a sequence of observations into a measurable relationship between time, past values, and repeating cycles. It is useful when you need interpretable drivers rather than a black‑box forecast. The fitted coefficients quantify baseline level, average drift per period, and persistence effects from one step to the next. This supports planning, anomaly review, and scenario testing using the same consistent framework. It works well for business and science.
The calculator lets you include a trend term t, a lag‑1 term yₜ₋₁, and optional seasonal indicators. Trend captures long‑run direction. Lag‑1 captures inertia and reduces serial correlation in residuals. Seasonal dummies capture systematic differences between recurring buckets, such as months or quarters, while keeping the model linear and explainable. If you have limited history, start simple and add one feature at a time.
Interpret coefficients in the scale of your data. A positive trend coefficient means the expected value rises each period, holding other terms constant. A lag coefficient near 1 indicates strong persistence and slower reversion after shocks. Compare R², RMSE, MAE, and MAPE together; lower errors often matter more than a higher R² for forecasting accuracy. Use the same horizon and sample window when comparing option sets.
The fitted table shows actual y, fitted ŷ, and residual e = y − ŷ for each period. Look for residual runs of the same sign, sudden jumps, or widening spread over time. Those patterns suggest missing predictors, a structural break, or non‑constant variance. Adjust options, shorten the sample, or model seasonality to improve stability. When residuals are centered and pattern‑free, the model is capturing the main signal.
Forecasts extend the design matrix into future periods. With lag enabled, forecasts are recursive, meaning each new prediction becomes the next lag input. This matches common operational forecasting workflows and produces smooth projections when persistence is high. Export CSV for deeper analysis, or PDF for stakeholder updates, including coefficients, headline metrics, and a concise preview of fitted rows and forward projections. Document your chosen settings so results are repeatable.
Provide one row per period with a label and a numeric value, separated by a comma. Keep rows in chronological order so the time index and lag calculations align correctly.
Enable lag‑1 when the series shows persistence, where today’s value is strongly related to yesterday’s. It often improves forecasts and reduces patterned residuals, but it also drops the first row from fitting.
Seasonality creates indicator variables for repeating buckets, such as months or quarters. Each dummy compares its bucket to the reference bucket, helping the model adjust for recurring level shifts without changing the trend interpretation.
If the data has almost no variation, R² is not meaningful. R² can also be low while forecasts are still useful. Focus on RMSE, MAE, and MAPE for practical accuracy across time.
RMSE measures typical error size in the same units as your data. A large RMSE indicates the model is missing key structure, the series is noisy, or the scale is large. Try lag or seasonality, or review outliers.
Forecast reliability depends on stable patterns. Sudden regime changes, new policies, or shocks can break historical relationships. Use forecasts as a baseline, monitor residuals, and refresh the model when new data arrives.
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.