How can I find the best p values using NLINFIT and Minkowski?

Hi,

I have several data gathered from a video quality experiment, and I'd like to check them using following expression:

yhat = ( (beta(1)*x(:,1)).^p + (beta(2)*x(:,2)).^p + (beta(3)*x(:,3)).^p).^(1/p);

I put beta0 = [1 1 1] as guess values, but I'm confusing in how can I find the best p values?

I put p inside beta0, as beta0 = [1 1 1 1] and I changed the expression to: yhat = ( (beta(1)*x(:,1)).^beta(4) + (beta(2)*x(:,2)).^beta(4) + (beta(3)*x(:,3)).^beta(4)).^(1/beta(4));

My question is: does this make sense?