Prediction Results
Model metrics, intervals, diagnostics, predictions, and exports.
Regression Equation
Training Metrics
Testing Metrics
Coefficient Statistics
Model Diagnostics
Predictor Correlation Matrix
Coefficient Covariance Matrix
New Predictions
Observation Results
Model Comparison
Calculation Steps
Formula Used
Multiple regression combines an intercept with weighted predictor values. Polynomial models add powers and optional interaction terms. Regularised models shrink coefficients to control unstable fits.
ŷ = b₀ + b₁x₁ + b₂x₂ + … + bₚxₚ Ridge: minimise Σ(y - ŷ)² + αΣbⱼ² Lasso: minimise Σ(y - ŷ)² + αΣ|bⱼ| Elastic Net: minimise Σ(y - ŷ)² + α[(1-r)Σbⱼ²/2 + rΣ|bⱼ|]
How to Use
- Paste training data with column headers.
- Select the target variable and regression model.
- Choose scaling, missing-value, split, and validation options.
- Enter new predictor rows using matching headers.
- Calculate and review predictions, intervals, metrics, and diagnostics.
- Export the prediction table as CSV or PDF.
Example Data
| Experience | Education Years | Projects | Salary |
|---|---|---|---|
| 1 | 12 | 2 | 32000 |
| 3 | 16 | 5 | 47000 |
| 5 | 18 | 9 | 65000 |
| 8 | 20 | 16 | 94000 |
Frequently Asked Questions
What does a regression prediction represent?
It estimates a numeric target from one or more predictors. The value depends on the fitted relationship and supplied inputs.
Which regression model should I choose?
Start with linear regression for an interpretable baseline. Use polynomial terms for curvature and regularisation for unstable coefficients.
What is the difference between confidence and prediction intervals?
A confidence interval estimates the mean response. A prediction interval is wider because it includes individual observation noise.
Why can R-squared be high while errors remain large?
R-squared measures explained variation, not absolute error size. Review RMSE and MAE alongside R-squared.
What does adjusted R-squared do?
It penalises unnecessary predictors. It can decrease when added variables do not improve the model enough.
Why standardise predictors?
Standardisation places numeric predictors on comparable scales. It is especially important for Ridge, Lasso, and Elastic Net.
How are categorical values handled?
The calculator automatically creates indicator columns for observed categories. Unseen prediction categories are flagged and treated as zero indicators.
What is multicollinearity?
Multicollinearity occurs when predictors overlap strongly. It can inflate coefficient uncertainty and make estimates unstable.
Can I predict outside the training range?
Yes, but extrapolation is risky. The calculator warns when numeric prediction values exceed observed training ranges.