Programming a simple function for estimating regression?

Write a MATLAB function which, given the input vectors x and y, containing the values xi and yi, respectively, and a natural number n, will find the least-squares approximation with the basis functions fj(x) = x^(i-1), j = 1,...,n, and return the vector a of the regression parameters aj and the value of the minimum total squared error E. Use your function for input variables x = l:length(vec), y = vec, and n=3. Include a plot of the input data points and the resulting estimation function y(x).

(((vec = [8 3 5 6 6 7 12 16 13 9 11 15 20] ))).

(((The data points are given by (xi,yi), i = 1,...,m in the form y(x) = sum (to n from j = 1) of ajfj(x), where fj(x) are the basis functions and aj are the regression parameters obtained by minimising the total squared error E = sum (to m from i = 1) of (yi - y(xi) )^2 ))).

Where I am struggling is that I am not allowed to use polyval or polyfit, as it needs to be as efficient as possible.

By the way, I have no idea where to start, which is why I haven't included anything else, so any help would be appreciated.