The linear model takes an input vector of dimension d and computes

g = Sum(i=1,d,w_i*x_i)-t

The w_i are called weights and t is the threshold.

A good error function is:

E(w_i,t)=Sum(n=1,N,(g_wt(x_n)-y_n)^2)

To solve for the optimal w_i and t, take

dE/dw_i = 0
and dE/dt = 0

and solve for w_i and t