The Longstaff-Schwartz algorithm involves a choice of basis functions. Suppose we have n + 1 dependent variables {y_i}ⁿ_i=0 to fit corresponding to the explanatory variables {x_i}ⁿ_i=0 Show that a polynomial of degree n can pass through all these points. However, by considering the behaviour of such a polynomial, discuss how there is a danger of over-fitting when we use the Longstaff-Schwartz algorithm with polynomial powers that are too high.