Show that the best least squares fit to a set of measurements $\displaystyle y_1,...y_m$ by a horizontal line y = $\displaystyle \lambda$ (where $\displaystyle \lambda$ is a constant) is their average:

$\displaystyle \lambda = \frac{y_1 + ... + y_m}{m}$

Other than that I need to use normal equations and that this is a problem concerning orthogonality, I am completely stuck and have no idea how to proceed. Can anyone help? Thanks.