The article provides a detailed exploration of implementing linear regression using three different approaches: from scratch with NumPy, with PyTorch tensors, and using PyTorch's built-in functions. Initially, the article delves into the mechanics of linear regression, emphasizing the importance of understanding gradient descent and calculating derivatives, particularly the mean squared error for optimization. The first implementation with NumPy involves manually coding the necessary functions, including the error calculation and gradient descent. Transitioning to PyTorch, the article demonstrates how to achieve the same using tensors, highlighting the differences in handling gradients. Finally, the article simplifies the process by leveraging PyTorch's built-in functions, such as MSELoss and SGD, to streamline the implementation and reduce the need for manual calculations, thereby illustrating the evolution from foundational understanding to utilizing advanced libraries for efficiency.