Abstract: Residual analysis is a commonly used technique for model checking in regression. However the problem gets more complicated when the dimension of covariate is high because it is difficult to see what the residuals should be plotted against. In this paper, we propose a simple search for a good projection direction for plotting and for constructing a lack-of-fit test. We also investigate the bootstrap approximation for computing-values.
Key words and phrases: Bootstrap approximation, dimension-reduction, empirical process, model checking, residual plot.