Example with interactions

If we have the next function:

$$\begin{equation} f(X^1, X^2) = (X^1 + 1)\cdot X^2 \end{equation}$$

• $X^1$ and $X^2$ are uniformly distributed over the interval $[-1,1]$
• $X^1$ and $X^2$ are perfectly correlated, i.e., $X^2 = X^1$.
• The sum of the 8 observed values is equal to 0.

i	1	2	3	4	5	6	7	8
$X^1$	-1	-0.71	-0.43	-0.14	0.14	0.43	0.71	1
$X^2$	-1	-0.71	-0.43	-0.14	0.14	0.43	0.71	1
$y$	0	-0.2059	-0.2451	-0.1204	0.1596	0.6149	1.2141	2