When to use Chauvenets or similar criterions - regression model data

I am wondering if I can use Chauvenets criterion for a data-set of 240 measurements of one y variables in order to detect outliers. I assume that the ys have a nonlinear relationship in parameters with about 12 x-variables. In general I did not quite understand on which y data the criterion is performed. Would you perform it on your complete set of y-variables, even if you assume a simple linear model with a small number of x-variables. I assumed that expected value and variance vary with the value of x, so I thought you would only perform it on a set of y variables which do not differ in x. Am I right?