# MAE

*English translation by SOTA – AI Community of the Russian original. Organisers who would like this translation removed can email sota.ai.community@gmail.com.*

All-Russian School Olympiad in Informatics 2025–2026, Regional Stage, Grades 9–11<br>
“Artificial Intelligence” profile, Tour 1, 17 January 2026<br>
Task D

**Points for the task:** 50<br>
**Answer submission format:** entering the answer<br>
**Number of attempts:** 10<br>
**Submission that counts:** the last one

## Statement

There is a sample of $N = 14$ observations (shown in the figure). Each point is given by a pair of coordinates $(x_i, y_i)$.

Consider the linear prediction $\hat{y}(x) = a \cdot x + b$. Find the minimum

$$
MAE = \frac{1}{N} \sum_{i=1}^{N} |\hat{y}(x_i) - y_i|
$$

of this prediction on the sample $(x_i, y_i)$ over all $a, b$.

![Scatter plot of the 14 observations on a grid, x from 0 to 11, y from 0 to 8](https://yastatic.net/s3/contest/roi/2026/ml/day1/final_with_grid.png)

*Translator's note: the figure above is the copy published with the official editorial; it is the same image as in the original statement. Read from its grid, the 14 points are $(0, 0)$, $(0, 2)$, $(0, 7)$, $(0, 8)$, $(4, 4)$, $(4, 7)$, $(6, 1)$, $(6, 5)$, $(9, 0)$, $(9, 1)$, $(9, 4)$, $(9, 7)$, $(11, 2)$ and $(11, 6)$.*

## Output format

Round the answer to 6 decimal places, using a point as the decimal separator.

## Scoring

An exact match of the answer: 50 points.

Test results are **not available** during the tour.