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