Univariate Linear Regression Using Gradient Descent Method

This implementation performs univariate linear regression using gradient descent method on a provided dataset. The algorithm estimates the relationship between variables by minimizing the error function through iterative optimization. Gradient descent is a fundamental optimization technique that progressively approaches the minimum of the error function through repeated iterations. As one of the most widely used methods in machine learning, it serves both prediction and classification tasks. The complete implementation with data and source code follows these key steps:

1. Collect a dataset containing both independent and dependent variables, typically stored in arrays or matrices for computational processing.

2. Define the error function using Mean Squared Error (MSE) formulation: MSE = (1/n) * Σ(y_pred - y_actual)², where n represents the number of data points.

3. Initialize model parameters (slope and intercept) with random values or zeros, setting up variables for the linear equation y = mx + b.

4. Implement gradient descent iterations by calculating partial derivatives of the error function with respect to each parameter, then updating parameters using: parameter = parameter - learning_rate * gradient. This process continues until convergence criteria are met.

5. Utilize the optimized parameters for making predictions or classifications by applying the trained linear model to new data points.

Through gradient descent-based univariate linear regression, we can effectively quantify relationships within data and develop predictive models for future observations and classification scenarios.