OLS with Robust Standard Errors and Diagnostics
Run an econometric OLS regression and choose the standard errors your field expects: heteroskedasticity-robust, clustered or Newey-West. A full battery of specification tests checks heteroskedasticity, functional form, autocorrelation, normality and multicollinearity.
Updated · By Bibin XavierData 500 × 11
| IDnumeric | Log_Wagenumeric | Educationnumeric | Experiencenumeric | Femalenumeric · coded | Unionnumeric · coded | Distance_Collegenumeric | Father_Educnumeric | Employednumeric · coded | Doctor_Visitsnumeric | Agenumeric |
|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 2.47 | 12 | 0 | 0 | 0 | 5.7 | 9 | 0 | 1 | 18 |
| 2 | 1.83 | 14 | 21 | 0 | 1 | 0 | 9 | 1 | 0 | 41 |
| 3 | 2.56 | 11 | 12 | 0 | 0 | 0 | 12 | 0 | 0 | 29 |
| 4 | 2.02 | 10 | 14 | 0 | 0 | 27.2 | 13 | 0 | 0 | 30 |
| 5 | 1.75 | 12 | 21 | 1 | 1 | 21.6 | 9 | 1 | 1 | 39 |
| 6 | 2.73 | 10 | 10 | 0 | 0 | 0 | 9 | 1 | 0 | 26 |
| 7 | 1.54 | 11 | 14 | 1 | 0 | 13.8 | 10 | 0 | 0 | 31 |
| 8 | 1.46 | 11 | 9 | 1 | 1 | 7.2 | 8 | 1 | 2 | 26 |
Variables and options
Results
500 rows · example dataCoefficients (Robust HC1 standard errors)
| Variable | Coefficient | SE | t | p | 95% CI |
|---|---|---|---|---|---|
| Constant | 0.8514 | 0.1637 | 5.202 | < .001 | [0.5298, 1.1730] |
| Education | 0.1073 | 0.0133 | 8.057 | < .001 | [0.0811, 0.1334] |
| Experience | 0.0218 | 0.0036 | 6.056 | < .001 | [0.0147, 0.0289] |
| Female | -0.2007 | 0.0514 | -3.902 | < .001 | [-0.3017, -0.0996] |
| Union | 0.0734 | 0.0665 | 1.104 | .270 | [-0.0572, 0.2039] |
Specification tests
| Test | Null hypothesis | Statistic | p | Result |
|---|---|---|---|---|
| Breusch-Pagan (Koenker) | Homoskedasticity | LM(4) = 24.116 | < .001 | Heteroskedasticity |
| White | Homoskedasticity | LM(12) = 27.731 | .006 | Heteroskedasticity |
| Ramsey RESET (powers 2, 3) | Correct functional form | F(2, 493) = 0.143 | .867 | Not rejected |
| Breusch-Godfrey | No autocorrelation up to lag 2 | LM = 1.089 | .580 | Not rejected |
| Durbin-Watson | No first-order autocorrelation | 2.028 | — | Close to 2 |
| Jarque-Bera | Normal residuals | JB = 4.193 | .123 | Not rejected |
Note. Condition number = 17.0 (above 30 suggests collinearity). Autocorrelation tests matter only when the rows are ordered in time.
Variance inflation factors
| Variable | VIF | 1 / VIF |
|---|---|---|
| Education | 1.00 | .998 |
| Experience | 1.01 | .995 |
| Female | 1.00 | .999 |
| Union | 1.01 | .994 |
Residuals against fitted values
Interpretation
Significant regressors: Education, Experience, Female. Heteroskedasticity is present, so the robust standard errors you selected are appropriate. The functional form passes the RESET test.
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). OLS with Robust Standard Errors and Diagnostics [Web application]. FreeStatisticalTools.com. https://freestatisticaltools.com/robust-standard-errors-regression-diagnostics/
BibTeX
@software{xavier_regressiondiagnostics_2026,
author = {Xavier, Bibin},
title = {OLS with Robust Standard Errors and Diagnostics},
publisher = {FreeStatisticalTools.com},
year = {2026},
url = {https://freestatisticaltools.com/robust-standard-errors-regression-diagnostics/},
note = {Web application}
}Suggested sentence for your methods section: “The analysis was carried out with the free OLS with Robust Standard Errors and Diagnostics tool on FreeStatisticalTools.com (Xavier, 2026).”
What is regression with robust standard errors?
Econometric regression needs more than coefficients. This tool estimates OLS with the standard errors your data require, heteroskedasticity-robust, clustered or Newey-West, and runs the standard specification tests for heteroskedasticity, functional form, autocorrelation, normality and multicollinearity.
When to use regression with robust standard errors
Use it for any cross-section or time-series regression where you need to justify the standard errors and show that the model passes standard specification tests.
Assumptions
- Linearity in parameters and no perfect collinearity.
- Exogenous regressors; if a regressor is endogenous, use 2SLS.
- Robust standard errors fix inference under heteroskedasticity, not bias from omitted variables.
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 dependent variable and regressors.
- Set the options. Fill in standard errors and breusch-godfrey lags.
- 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 regression with robust standard errors in APA style
Report coefficients with the type of standard errors, R², the F test and the diagnostic tests in a note or appendix table.
Frequently asked questions
When should I use robust standard errors?
Whenever the Breusch-Pagan or White test suggests heteroskedasticity, and by default in most applied economics. HC1 matches Stata’s robust option; HC3 performs better in small samples.
When do I need clustered standard errors?
When observations are grouped (students in schools, firms in industries, repeated observations of the same unit) and errors may be correlated within groups.
What does the Ramsey RESET test show?
It tests whether powers of the fitted values add explanatory power. A significant result suggests omitted non-linearities or variables.
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