Multiple Regression Virtual Lab

Master multivariate regression through interactive experimentation

⚡

🌟 Enhanced Training

Full hyperparameter control & visualization

🌾

Crop Price Forecasting

Predict agricultural prices

📊

Demand Prediction

Forecast product demand

📈

Linear Model

Multiple features regression visualization

⚖️

Feature Scaling

Normalization and standardization

🔄

Polynomial Features

Non-linear relationships modeling

🎯

Regularization

Ridge, Lasso, and Elastic Net

📈 Enhanced Regression Training - Gradient Descent Optimizer

Train regression models with different regularization techniques. Watch coefficients evolve and compare MSE, R², and MAE metrics in real-time.

⚙️ Model Configuration

Regression Type

Regularization method

Learning Rate: 0.01

Gradient descent step size

Epochs: 50

Training iterations

Polynomial Degree: 1

Feature polynomial expansion

🎮 Training Controls

Speed:

Epoch 0 / 500.0%

Train MSE

0.0

Val MSE

0.0

Train R²

0.000

Val R²

0.000

Train MAE

0.0

📊 Training Metrics

MSE Loss Curves

R² Score

Feature Coefficients (Epoch 0)

📋 Training History

Epoch	Train MSE	Val MSE	Train R²	Val R²	MAE

📐 Linear Regression Equations

Multiple Regression Model:

\hat{y} = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + ... + \beta_p x_p

MSE Loss:

\text{MSE} = \frac{1}{n}\sum_{i=1}^{n}(y_i - \hat{y}_i)^2

R² Score:

R^2 = 1 - \frac{\sum(y_i - \hat{y}_i)^2}{\sum(y_i - \bar{y})^2}

Gradient Descent Update:

\beta_j \leftarrow \beta_j - \alpha \frac{\partial \mathcal{L}}{\partial \beta_j}

💡 Understanding Regression

• Linear (OLS): No regularization, minimizes MSE directly
• Ridge (L2): Shrinks coefficients, prevents overfitting, keeps all features
• Lasso (L1): Can zero out coefficients, performs feature selection
• Elastic Net: Combines L1 and L2, best of both worlds
• R² Score: 1.0 = perfect fit, 0.0 = no better than mean prediction
• Polynomial Degree: Higher degrees capture non-linear patterns but risk overfitting