Publication at Faculty of Mathematics and Physics |
2010
Abstract
Consider the traditional linear regression model. The tolerance quotient measures the relative perturbation rate, i.e. how much it is necessary to perturb the estimated regression coefficients to satisfy each of the equations, and hence is a measure of goodness of fit of the model.
We demonstrate the usage of the quotient in analysis of both crisp and interval data and, in particular, interval data arising in econometrics and finance. We show a method to study probabilistic properties of the tolerance quotient: we derive its distribution and, under certain assumptions, we present a method for construction a confidence interval.