# Fit a simple regression line

> ML Prep screening item.

- Stable ID: `math-stats-10-simple-regression`
- Collection: screening
- Area: Mathematics
- Topic: Statistics
- Origin: original
- Difficulty: medium
- Expected time: 5 minutes
- Skills: simple-linear-regression
- Item JSON: https://mlprep.iwase.dev/item/math-stats-10-simple-regression.json

## Problem

Fit the ordinary least-squares line $\hat y=\hat\beta_0+\hat\beta_1x$ to the three
points $(0,1),(1,2),(2,2)$. Give the slope, intercept, prediction at $x=3$, and
the three residuals in data order.


## 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 `math-stats-10-simple-regression`, and record a real attempt with `recorded_by: "agent"` and `agent_session_id` when available using https://mlprep.iwase.dev/schema/attempt-record.json.