Panel Data Regression: Fixed and Random Effects
Estimate the standard panel data models in one run and let the specification tests pick between them. Fixed effects control for unobserved, time-invariant differences between entities; random effects assume those differences are unrelated to the regressors.
Updated · By Bibin XavierData 480 × 8
| Firmtext · 60 levels | Yearnumeric | Industrytext · 3 levels | ROAnumeric | Leveragenumeric | Log_Sizenumeric | RnD_Intensitynumeric | GDP_Growthnumeric |
|---|---|---|---|---|---|---|---|
| F01 | 2016 | Manufacturing | 11.28 | 0.67 | 8.45 | 0.08 | 1.63 |
| F01 | 2017 | Manufacturing | 14.97 | 0.56 | 7.91 | 0.12 | 1.8 |
| F01 | 2018 | Manufacturing | 12.24 | 0.63 | 7.78 | 0.1 | 2.39 |
| F01 | 2019 | Manufacturing | 11.1 | 0.78 | 7.44 | 0.08 | 1.93 |
| F01 | 2020 | Manufacturing | 11.04 | 0.75 | 7.65 | 0.09 | 2.13 |
| F01 | 2021 | Manufacturing | 11.33 | 0.68 | 7.88 | 0.09 | 1.18 |
| F01 | 2022 | Manufacturing | 13.01 | 0.66 | 7.84 | 0.11 | 1.28 |
| F01 | 2023 | Manufacturing | 13.76 | 0.69 | 8.1 | 0.1 | 1.9 |
Variables and options
Results
480 rows · example dataPanel regression estimates
| Variable | Pooled OLS | Fixed effects | Random effects | Two-way FE | First differences |
|---|---|---|---|---|---|
| Leverage | -3.4302*** (0.6815) | -5.9077*** (0.7248) | -3.4921*** (0.6831) | -5.9668*** (0.7151) | -6.7783*** (0.8999) |
| Log_Size | 2.3195*** (0.1074) | 0.7130*** (0.1946) | 2.2820*** (0.1073) | 0.6164** (0.2190) | 0.8298** (0.2799) |
| RnD_Intensity | 35.1346*** (4.5217) | 16.2880** (5.2911) | 34.7101*** (4.4942) | 15.4763** (5.2894) | 19.1418** (6.4148) |
| GDP_Growth | 0.4235*** (0.1214) | 0.4327*** (0.1171) | 0.4280*** (0.1214) | 0.2014 (0.2568) | 0.4490** (0.1298) |
| R² (within) | — | .206 | — | .218 | — |
| R² (overall) | .747 | — | .695 | — | .229 |
Note. Standard errors in parentheses (clustered by entity). * p < .05, ** p < .01, *** p < .001. Random effects: Swamy–Arora, σu = 0.280, σe = 1.339. Constant terms omitted.
Model selection tests
| Test | Comparison | Statistic | p | Preferred model |
|---|---|---|---|---|
| F test for entity effects | Pooled OLS vs fixed effects | F(59, 416) = 2.824 | < .001 | Fixed effects |
| Breusch-Pagan LM | Pooled OLS vs random effects | χ²(1) = 0.636 | .425 | Pooled OLS |
| Hausman | Random vs fixed effects | χ²(4) = 89.361 | < .001 | Fixed effects |
Note. The Hausman test uses conventional covariance matrices; a negative statistic is set to zero. When it rejects, entity effects are correlated with the regressors and only fixed effects are consistent.
Interpretation
The tests point to the fixed effects model (Hausman p < .001). In that model, significant regressors are Leverage (-5.908), Log_Size (0.713), RnD_Intensity (16.288), GDP_Growth (0.433).
How to cite this tool
Using these results in a thesis, journal article, report or class assignment? Please cite this free tool so others can find it. It keeps the site free.
APA 7
Xavier, B. (2026). Panel Data Regression: Fixed and Random Effects [Web application]. FreeStatisticalTools.com. https://freestatisticaltools.com/panel-data-regression-fixed-random-effects/
BibTeX
@software{xavier_paneldataregression_2026,
author = {Xavier, Bibin},
title = {Panel Data Regression: Fixed and Random Effects},
publisher = {FreeStatisticalTools.com},
year = {2026},
url = {https://freestatisticaltools.com/panel-data-regression-fixed-random-effects/},
note = {Web application}
}Suggested sentence for your methods section: “The analysis was carried out with the free Panel Data Regression: Fixed and Random Effects tool on FreeStatisticalTools.com (Xavier, 2026).”
What is panel data regression?
Panel data follow the same entities over several periods. Fixed effects models remove all time-invariant differences between entities; random effects models treat them as random draws, which is more efficient but requires them to be unrelated to the regressors.
When to use panel data regression
Use panel models when the same entities (firms, countries, people) are observed over several periods, to control for unobserved heterogeneity.
Assumptions
- Each entity-time pair appears once.
- Fixed effects need regressors that vary within entities over time.
- Use standard errors clustered by entity unless you have reason not to.
How to set up your data
Long format: one row per entity and period, with an entity identifier, a time variable, the outcome and the regressors.
How to use this tool
- Enter your data. Paste columns from Excel, Google Sheets or SPSS with variable names in the first row, or upload a CSV or Excel file. The example data shows the expected layout.
- Choose the variables. Select the entity (panel) identifier, time variable, dependent variable and regressors.
- Set the options. Fill in standard errors.
- Read the results. Results update automatically. Read the plain-English interpretation, then use Copy table to paste APA-style tables into Word and Copy for the results sentence.
How to report panel data regression in APA style
Report the chosen estimator with clustered standard errors and the Hausman, F and LM tests that justify it.
Frequently asked questions
Fixed effects or random effects?
Use the Hausman test: if it rejects, the entity effects are correlated with the regressors and fixed effects is the consistent choice.
What does the F test for entity effects show?
Whether entity effects are jointly significant. If it rejects, pooled OLS is inappropriate.
Why cluster standard errors by entity?
Errors of the same entity are typically correlated over time; clustering keeps inference valid under this serial correlation and heteroskedasticity.
Related tools
Browse all categories
Data cleaning and preparation · Describe and explore · Compare means · Nonparametric tests · Correlation and regression · Bayesian statistics · Categorical data · Reliability and agreement · Multivariate analysis · Structural equation modeling · Econometrics and time series · Panel data and causal inference · Marketing and decision research · Survival, clinical and meta-analysis · Study planning and calculators · PLS-SEM