Calculator Form
Example Data Table
| y | x1 | x2 | x3 | x4 |
|---|---|---|---|---|
| 92 | 12 | 80 | 4 | 18 |
| 88 | 10 | 74 | 3 | 17 |
| 76 | 8 | 66 | 5 | 14 |
| 95 | 13 | 82 | 4 | 19 |
Formula Used
The calculator uses ordinary least squares for each candidate model.
Coefficient estimate: β = (X'X)-1X'y
Predicted value: ŷ = β0 + β1x1 + β2x2 + ... + βkxk
SSE: Σ(y - ŷ)2
AIC: n × ln(SSE / n) + 2k
BIC: n × ln(SSE / n) + k × ln(n)
Adjusted R Squared: 1 - [(1 - R2) × (n - 1) / (n - k)]
How to Use This Calculator
- Paste numeric CSV data into the data box.
- Use the first row as column headers.
- Enter the dependent column name.
- Enter candidate predictors separated by commas.
- Choose forward, backward, or both selection.
- Select AIC, BIC, adjusted R squared, or p value.
- Press Calculate to view the model above the form.
- Use CSV or PDF export for saving results.
Stepwise Regression Calculator Guide
Purpose
A stepwise regression calculator helps you explore many predictors without building every model by hand. It tests variables in ordered steps. Each step compares fit, penalty, and usefulness. The goal is not blind automation. The goal is guided screening before deeper statistical review.
Selection Methods
Stepwise selection is useful when a dataset has several possible inputs. Forward selection starts with no predictors. It adds the strongest candidate first. Backward elimination starts with every candidate. It removes the weakest variable first. Both mode combines adding and removing, so the final set can change after each move.
Model Scoring
This calculator uses ordinary least squares. It estimates coefficients that reduce squared residual error. It can compare AIC, BIC, adjusted R squared, or p values. AIC favors useful fit with a modest penalty. BIC applies a stronger penalty as sample size grows. Adjusted R squared rewards fit, but penalizes unnecessary predictors. P value mode checks whether a coefficient looks meaningful after other variables are included.
Data Preparation
Good data preparation matters. Each column should have one clear header. Missing values should be fixed before analysis. Extreme outliers should be reviewed because they can pull the fitted line. Strongly correlated predictors may also cause unstable coefficients. In that case, choose variables using domain knowledge, not only automatic scores.
Interpreting Results
The results show selected predictors, coefficients, fit measures, and a step log. The equation helps you see how each predictor changes the expected outcome. The root mean squared error shows typical prediction error in response units. The coefficient table also shows standard errors and approximate p values.
Best Practice
Use stepwise regression as an exploration tool. It is not proof of cause. A chosen variable can still be misleading. Validate the final model with new data when possible. Also check residual plots, assumptions, and practical meaning. A smaller model is often easier to explain. Yet it must still match the real problem.
Reporting
For reporting, save the results as CSV or PDF. Include the data source, chosen method, criterion, and thresholds. State that selection was automated. Then explain why the final predictors make sense.
Before publishing a model, rerun it after removing errors. Compare predictions against known outcomes. This final check helps reveal overfitting, leakage, and weak variable choices very early.
FAQs
What is stepwise regression?
Stepwise regression is a variable selection method. It adds or removes predictors through repeated model comparisons. The goal is to find a useful smaller model.
Which selection method should I use?
Use forward selection for many candidate predictors. Use backward elimination when you trust the full starting model. Use both when you want adding and removing checks.
What does AIC mean?
AIC compares model fit with a penalty for extra parameters. Lower AIC usually means a better balance between accuracy and simplicity.
What does BIC mean?
BIC is similar to AIC, but it penalizes larger models more strongly. It often selects fewer predictors, especially with larger datasets.
Can this calculator prove causation?
No. Stepwise regression finds statistical patterns. It does not prove cause. Use research design, controls, and subject knowledge for causal claims.
Why did a predictor get removed?
A predictor may be removed because it worsened the chosen criterion. In p value mode, it may exceed the stay threshold after other predictors enter.
Why do correlated predictors cause issues?
Highly correlated predictors can make coefficients unstable. One variable may appear important only because it overlaps strongly with another variable.
Should I validate the final model?
Yes. Test the chosen model on fresh data when possible. Validation helps detect overfitting and weak predictor choices.