Use lsqlin, IF you have the optimization toolbox.
Thus, if X is your nx7 design matrix, and Y an nx1 column vector, then the call to lsqlin would look like this:
lb = zeros(1,7);
ub = ones(1,7);
Aeq = ones(1,7);
beq = 1;
coef = lsqlin(X,Y,[],[],Aeq,beq,lb,ub);
There is no need to use a tool like fmincon as Amit has suggested. That tool is designed for nonlinear problems, which this is not. See that fmincon needs a starting value, and it will be considerably less efficient.
If you lack the optimization toolbox, this can still be solved using lsqnonneg, although that would require a transformation of the problem. Anyway, I'd strongly recommend a copy of that TB if you will do any work of this sort in the future.
