Model Results
Regression Equation
Coefficient Statistics
| Term | Coefficient | Std. Error | Statistic | p-value | Lower CI | Upper CI | VIF |
|---|
Degree Comparison
| Degree | Features | Train R² | Test R² | CV RMSE | RMSE | MAE | AIC | BIC | Assessment |
|---|
Predictions
Observation Diagnostics
| # | Actual | Predicted | Residual | Std. Residual | Leverage | Cook's D | Flag |
|---|
Fit Visualization
Actual Versus Predicted
Residuals Versus Fitted
Validation Error by Degree
Interpretation and Warnings
Formula Used
ŷ = β₀ + β₁x + β₂x² + ... + βd xᵈ OLS minimizes: Σ(yᵢ - ŷᵢ)² Ridge minimizes: Σ(yᵢ - ŷᵢ)² + λΣβⱼ² R² = 1 - SSE / SST Adjusted R² = 1 - (1 - R²)(n - 1)/(n - p - 1) RMSE = √[Σ(yᵢ - ŷᵢ)² / n] MAE = Σ|yᵢ - ŷᵢ| / n
How to Use
Paste numeric rows or upload a CSV file. Keep the target in one selected column. Remove invalid rows before fitting the model.
Choose the degree and fitting method. Adjust validation, preprocessing, and confidence settings. Submit the form to calculate results.
Review metrics, charts, coefficients, and warnings. Compare degrees before selecting a final model. Export results for later reporting.
Example Data
| x | y | Expected pattern |
|---|---|---|
| -2 | 9.4 | Higher response away from zero |
| 0 | 1.2 | Minimum near the center |
| 2 | 9.8 | Quadratic growth |
Frequently Asked Questions
What does polynomial degree mean?
The degree controls the highest feature power. Larger degrees capture more curved relationships. Excessive degrees can overfit small datasets.
How should I choose the degree?
Compare cross-validation error and testing performance. Prefer the simplest competitive model. Avoid choosing from training accuracy alone.
Why should predictors be standardized?
Polynomial powers can create large numeric differences. Standardization improves matrix stability. It also supports regularized model fitting.
What is an interaction term?
An interaction combines multiple predictors together. It models effects depending on another predictor. Enable interactions for multivariable datasets.
What does Ridge regression change?
Ridge shrinks unstable coefficient estimates. It often helps correlated polynomial terms. The lambda value controls shrinkage strength.
When is Lasso useful?
Lasso can set weak coefficients to zero. This creates a simpler feature set. Results depend strongly on preprocessing and lambda.
What is extrapolation?
Extrapolation predicts beyond observed predictor ranges. Polynomial curves can change rapidly there. Treat extrapolated values with extra caution.
Why are prediction intervals wider?
Prediction intervals include observation-level noise. Confidence intervals describe the mean response. New observations require more uncertainty.
What indicates overfitting?
Training performance remains extremely strong. Testing or validation performance becomes weaker. A simpler degree may generalize better.