Implement Linear Regression Gradient Descent
Company: Databricks
Role: Machine Learning Engineer
Category: Machine Learning
Difficulty: medium
Interview Round: Onsite
Implement simple linear regression from scratch using batch gradient descent.
Given training data with one input feature `x` and target `y`, fit a model of the form `y = w * x + b`. Define the loss function, derive the gradients with respect to `w` and `b`, show the update rules, and explain practical choices such as learning rate, initialization, stopping criteria, feature scaling, and how you would evaluate whether training has converged.
Quick Answer: This question evaluates understanding of simple linear regression, batch gradient descent, loss function formulation, gradient derivation for model parameters, and training diagnostics such as learning rate, initialization, stopping criteria, feature scaling, and convergence evaluation.