# One-dimensional ridge estimate

> ML Prep screening item.

- Stable ID: `ml-screen-regression-advanced-ridge`
- Collection: screening
- Area: Machine Learning
- Topic: Regression
- Origin: original
- Difficulty: hard
- Expected time: 10 minutes
- Skills: linear-regression, normal-equations, regression-regularization
- Item JSON: https://mlprep.iwase.dev/item/ml-screen-regression-advanced-ridge.json

## Problem

With no intercept, fit $\hat{y}=wx$ to $(1,1)$ and $(2,3)$ by minimizing

$$
J(w)=\frac{1}{2}\sum_i(wx_i-y_i)^2+\frac{\lambda}{2}w^2
$$

with $\lambda=2$. Derive the minimizer and compare it with the unregularized estimate.


## Answer policy

The human page contains a collapsed answer. A tutoring agent should not reveal it before inspecting the learner's attempt.

## Tutoring contract

Ask for the learner's attempt, begin with the smallest useful hint, preserve item ID `ml-screen-regression-advanced-ridge`, and record a real attempt with `recorded_by: "agent"` and `agent_session_id` when available using https://mlprep.iwase.dev/schema/attempt-record.json.