Calculator Form
Example Data Table
| Coefficient | Estimate | Std. Error | Method | Confidence Level | Family | Link |
|---|---|---|---|---|---|---|
| Intercept | 1.2300 | 0.3100 | Z | 95% | Binomial | Logit |
| Age | 0.0450 | 0.0120 | Z | 95% | Binomial | Logit |
| Treatment | -0.6800 | 0.2200 | T | 99% | Gaussian | Identity |
| Exposure | 0.4100 | 0.0950 | Z | 90% | Poisson | Log |
Formula Used
Wald confidence interval: Lower bound = Estimate − Critical Value × Standard Error
Upper bound: Upper bound = Estimate + Critical Value × Standard Error
Margin of error: Margin = Critical Value × Standard Error
Test statistic: Statistic = (Estimate − Null Value) ÷ Standard Error
Exponentiated interval: Exp(Lower), Exp(Estimate), and Exp(Upper)
The calculator uses a normal critical value for large sample GLM output. It can also use a t critical value when you prefer a degrees of freedom adjustment.
How to Use This Calculator
- Enter the coefficient name for clear reporting.
- Type the estimated GLM coefficient value.
- Enter the standard error from model output.
- Choose the confidence level, such as 95.
- Select normal or t critical value method.
- Enter degrees of freedom when using t.
- Add model family, link, sample size, and notes.
- Tick exponentiated output for odds ratios or rate ratios.
- Press Calculate Interval to show the results.
- Use the CSV or PDF button for exports.
About GLM Coefficient Confidence Intervals
Why this calculator matters
A GLM coefficient confidence interval helps you judge estimate precision. It shows a plausible range for the true model coefficient. Analysts use it in logistic, Poisson, Gamma, and Gaussian models. A narrow interval suggests stronger precision. A wide interval suggests more uncertainty.
What the interval means
This calculator applies the Wald interval method. It combines the coefficient estimate, its standard error, and a chosen critical value. The output reports lower and upper bounds on the coefficient scale. It also shows the test statistic, margin of error, and approximate p value.
When exponentiated values help
Exponentiated values are useful with logit and log links. In logistic regression, exp(coefficient) becomes an odds ratio. In Poisson regression, exp(coefficient) becomes a rate ratio. The transformed interval is often easier to interpret in reports and dashboards.
Choosing z or t
The normal method suits many large sample GLM settings. The t method can be useful when you want a degrees of freedom adjustment. This page lets you compare both approaches. That makes the tool more flexible for teaching, quality checks, and applied analysis.
Useful reporting details
The calculator also stores family, link, sample size, and notes. These fields improve documentation. You can export your result as CSV or PDF. That supports audit trails, team reviews, and reproducible statistical reporting. The layout stays simple, responsive, and easy to scan.
Best practice tip
Always interpret intervals with model context. Check variable coding, reference groups, and link function. Review practical importance, not only statistical significance. Clear confidence interval reporting leads to stronger decisions and better communication across technical and nontechnical teams.
Frequently Asked Questions
1. What does this calculator compute?
It computes a GLM coefficient confidence interval using the estimate, standard error, confidence level, and selected critical value method.
2. What is a Wald confidence interval?
A Wald interval uses estimate ± critical value × standard error. It is common in generalized linear model summaries and quick reporting workflows.
3. When should I exponentiate the coefficient?
Exponentiate when the link is logit or log and you want odds ratios or rate ratios. The calculator shows both transformed bounds.
4. Should I use z or t?
Z is common for larger samples and standard GLM output. T can be used when you want a degrees of freedom adjustment.
5. What does the p value here represent?
It is an approximate two-sided p value based on the calculated test statistic. It helps summarize evidence against the null value.
6. Can I use this for logistic regression?
Yes. Enter the logistic regression coefficient and standard error. Then use exponentiated output to view an odds ratio interval.
7. Can I export my result?
Yes. The page includes CSV and PDF download buttons after form submission. They export the current computed output values.
8. Why is my interval very wide?
Wide intervals often come from large standard errors, small samples, collinearity, sparse outcomes, or unstable model specification.