If there is a positive correlation between number of years studying math and shoe size (for children), does that prove that larger shoes cause more studying of math , or vice versa? Can you think of a hidden variable that might be influencing both of the other variables?

The hidden variable is age.

Step-by-step explanation:

That does not prove that larger shoes cause more studying math or vice versa.

The children with larger shoes are most probably older so they would have done more years of studying than the younger ones.

The hidden variable is the age of the child.