Linear regression: normal equation vs SGD

[ThomasHartDev]

adds linear regression solved two ways so you can see the tradeoff side by side. one path is the normal equation, the exact closed form where you set the gradient to zero and solve a small linear system, with optional ridge and a pseudoinverse fallback when the design matrix is collinear. the other is minibatch gradient descent, which standardizes the features first so a single learning rate works and then maps the weights back to the raw scale. tests check that both recover the true coefficients on clean data and land in the same place on noisy data, plus the usual edge cases (empty input, rank-deficient X, bad hyperparams). mostly a demo of ordinary least squares and why you'd reach for the iterative version once the feature count gets big.