Is this true or false?

Question

True or false.     The least-squares line must pass through at least one of the data points.

 

If you think the statement is true, then prove it. On the other hand, if you think the statement is false, then give an example that disproves the statement.

Answer 1

The data points consisting of the unit square {0,1},{1,0},{1,1},{0,0} is one such counter-example.