# Solve normal equations

> ML Prep screening item.

- Stable ID: `ml-screen-regression-standard-normal-equations`
- Collection: screening
- Area: Machine Learning
- Topic: Regression
- Origin: original
- Difficulty: medium
- Expected time: 8 minutes
- Skills: linear-regression, squared-loss, normal-equations
- Item JSON: https://mlprep.iwase.dev/item/ml-screen-regression-standard-normal-equations.json

## Problem

Fit $\hat{y}=b+wx$ by ordinary least squares to $(0,1)$, $(1,2)$, and $(2,2)$. Form $X^{\mathsf T}X$ and $X^{\mathsf T}y$ using an intercept column, then solve for $(b,w)$.


## 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-standard-normal-equations`, and record a real attempt with `recorded_by: "agent"` and `agent_session_id` when available using https://mlprep.iwase.dev/schema/attempt-record.json.