How to use the poisson regression calculator
Prepare the values for this calculation
Fit a one-predictor Poisson log-linear regression by Newton/IRLS. Use the formula below to check that it answers your question. Read the input units before transferring figures from a statement, measurement or dataset.
Enter and check each input
- x,count y pairs — one per line: keep one record per line and preserve the column order shown in the example. Replace the example data with your own complete dataset.
- x for predicted mean: enter a finite number. Use the unit named in the label or selected above. Do not leave this required field blank.
The input table gives a complete example. Keep units and time periods consistent across related fields.
Calculate and resolve any input error
Choose Calculate after entering the values. Changes also update the answer after a short pause. If an error appears, follow its message, correct the field and calculate again. Reset restores the example values.
Interpret the answer
Check Predicted count mean first. With the unchanged example inputs, it is 16. Compare the additional metrics with the primary result; each has its own label and unit.
Compare and keep a useful result
For a controlled comparison, keep every other example input unchanged and change x for predicted mean from 4 to 4.4. The resulting Predicted count mean is 21.112126572366. This illustrates the equation’s response to that input, rather than a forecast of real events.
Read the chart’s axis labels and data table. A scenario curve changes one stated input while holding the others fixed; it does not add external observations. Use Download graph to save an available chart as a PNG.
Use Copy result or Download CSV to keep the answer. Share tool shares the page address without placing your input values in the URL. Recheck inputs and assumptions before using the result for a decision.
Poisson Regression Calculator formula
log(E[Y|x])=β₀+β₁x, with Poisson variance equal to the fitted mean.
Inputs and units
| Input | Format / range | Example |
|---|---|---|
| x,count y pairs — one per line | One row per line | 0,1
1,2
2,4
3,8 |
| x for predicted mean | Number | 4 |
Worked example
Using the example inputs above, the predicted count mean is 16.
- Predicted count mean
- 16
- Intercept β₀
- 7.772141417652e-17
- Slope β₁
- 0.69314718056
- Rate ratio per x unit
- 2
Results and assumptions
The output uses the predicted count mean convention and formula shown above. Match the entered units and source assumptions when comparing results.
Fix an input or unexpected result
x for predicted mean is required. Enter x for predicted mean using the format and bounds in the input table. Zero and an empty field are different: use zero only if it is allowed and represents your data.
If your answer differs from the example, choose Reset and compare every field, including selected units and options. Check percentage versus decimal entry and whether values describe the same period. Round only the final displayed answer when reproducing the formula.
If a discrepancy remains, report the calculator issue with the page address, non-sensitive example inputs, actual result, expected result and a reference for your calculation.