Calculator Inputs
Paste panel data in CSV format. The model removes each entity's fixed effect by demeaning.
Example Data Table
| Entity | Time | Y | X1 | X2 |
|---|---|---|---|---|
| A | 1 | 12 | 5 | 2 |
| A | 2 | 14 | 6 | 3 |
| A | 3 | 15 | 7 | 4 |
| B | 1 | 10 | 4 | 1 |
| B | 2 | 11 | 5 | 1.5 |
| C | 1 | 20 | 8 | 5 |
Formula Used
Within transformation: \( y_{it} - \bar{y}_i = \beta_1(x_{1it} - \bar{x}_{1i}) + \cdots + \beta_k(x_{kit} - \bar{x}_{ki}) + (u_{it} - \bar{u}_i) \)
The estimator subtracts each entity mean from every row. This removes all time-invariant entity-specific effects before running ordinary least squares.
Coefficient estimator: \( \hat{\beta} = (X_w'X_w)^{-1}X_w'y_w \)
Entity effect recovery: \( \hat{\alpha}_i = \bar{y}_i - \hat{\beta}'\bar{x}_i \)
Within R-squared: \( R^2_{within} = 1 - SSE/SST \), using demeaned outcomes and fitted demeaned values.
How to Use This Calculator
- Paste a panel dataset into the textarea with comma-separated columns.
- Enter the entity column and optional time column names.
- Choose one dependent column and one or more regressors.
- Click the submit button to estimate the within model.
- Review coefficients, entity effects, fitted values, and chart output.
- Download CSV files or generate a PDF report.
Time-invariant or perfectly collinear transformed regressors cannot be estimated. Add variation or remove redundant columns if needed.
Frequently Asked Questions
1. What does fixed effects regression estimate?
It estimates how changes within the same entity relate to changes in the outcome. Stable unobserved differences across entities are removed before estimating slopes.
2. Why are time-invariant regressors not estimated?
After demeaning, a variable that never changes within an entity becomes zero in every transformed row. With no within variation, its coefficient is unidentified.
3. What is within R-squared?
Within R-squared measures explained variation after removing entity means. It focuses only on fit inside entities, not differences between entity levels.
4. Can I enter multiple regressors?
Yes. Separate the independent column names with commas. Every selected regressor must be numeric and should vary within at least some entities.
5. Is the time column mandatory?
No. It is optional here and mainly helps label rows and charts. The estimator only needs an entity identifier and numeric observations.
6. What causes the singular matrix message?
It usually means one transformed regressor duplicates another or loses all usable variation after demeaning. Remove redundant variables or add better data.
7. Are the p-values exact?
This page reports approximate two-sided p-values using a normal reference. They are useful for screening, though specialized econometric software is stronger for formal inference.
8. When should fixed effects be preferred?
Use it when hidden differences across entities may bias pooled estimates, but those differences remain roughly constant over time within each entity.