with a set of k unknown parameters (regression coef cients) β ¼ β1;…; βk. 1 1 n n
For a set of observed data with pairs y ; x ; …; y ; x with no error associated to the response or predictor, Eq. (12) applies as the ideal case. However, since measurement errors will make the pairs to be out of the fitting function, at the best case Eq. (11) will be correct only on average. Therefore, Eq. (12) can be expressed as a mean function by