5.2 Linear regression from scratch
You can implement, fit and interpret a linear model without sklearn.
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Linear regression is the first complete model — a loss, a fit, an interpretation — and implementing it from scratch, closed form and gradient descent both, sets the template every later model follows. It sits first in the modelling run for exactly that reason. The interpretive rule arrives with it: a coefficient describes association within this dataset and this feature set, and reading it as a lever to pull is the oldest mistake in applied statistics.
Work through these
Model, loss, closed form and gradient descent
The model, the quantity being minimised, and two ways of finding the minimum: solving directly, or descending iteratively. Implementing both is what makes every later model understandable.
Assumptions and residual diagnostics
Linear regression assumes several things about the errors, and the residuals are how you check them. Skipping this is how confident wrong conclusions get published.
Interpreting coefficients honestly
A coefficient describes a change holding everything else fixed, which is rarely how the world moves. Stating it honestly is what separates a careful analyst from a confident one.
Polynomial and basis expansion
Adding powers and transformed versions of the features keeps the model linear in its parameters while fitting curves. It is the cheapest way to escape the straight-line assumption.
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