Multivariate Linear Regression

A simple implementation of multivariate linear regression using gradient descent, built with NumPy and Matplotlib.

Contents

1. Feature Matrix Creation: Generates random feature vectors with multiple variables ($x_1$, $x_2$)
2. Target Generation: Creates synthetic data with linear relationship $y = \theta_0 + \theta_1 x_1 + \theta_2 x_2 + noise$
3. Cost Function: Calculates Mean Squared Error between predictions and true values
4. Gradient Descent: Iteratively finds optimal parameters $\theta_0$, $\theta_1$, and $\theta_2$
5. 3D Visualization: Shows data points and fitted plane in 3D space

Generated Plots

1. 3D Data Scatter Plot

Shows the synthetic data points distributed in 3D space with two features ($x_1$, $x_2$) and target values ($y$).

2. Cost Function Progress

Displays the cost reduction over iterations during gradient descent optimization.

3. Final Model Evaluation

Shows the original data points with the fitted regression plane in 3D.