# Error metric for a regression model with two dependent variables

I'm working on an algorithm that estimates two parameters of its input data. I have a representative set of samples with the true parameters, to act as a ground truth. As this algorithm uses a threshold that has to be adjusted manually by the user, I was wondering if it could be possible to use my "ground truth" samples to find the best threshold for my training set. How can I express an error metric for two dependant variables, since for each threshold value and sample I'll have two parameters estimated by the algorithm.

I would really appreciate any hint.

Since you know the true parameters, you could calculate the difference of estimated value and true parameter. Sum of squares of this difference would be a good error metric. i.e. say $\hat\theta_1, \hat\theta_2,\dots,\hat\theta_n$ are estimates and $\theta_1,\theta_2,\dots, \theta_n$ are the true values. Then take $E = \sum_{i=1}^{n}(\hat\theta_i-\theta_i)^2$. You could consider sum (or weighted sum) of E=E1+E2 in case of two parameters.